1"use strict";(self.webpackChunk=self.webpackChunk||[]).push([[3735],{1295(A,e,t){t.d(e,{z:()=>o});var i=t(96540),g=t(53259),n=t.n(g),r=(t(78478),t(74848)),a=n()({loader:function(){return t.e(1236).then(t.bind(t,91236))},loading:function(A){return A.timedOut?(0,r.jsx)("blockquote",{children:"Error: Loading Plotly timed out."}):(0,r.jsx)("div",{children:"loading..."})},timeout:1e4}),o=i.memo(function(A){var e=A.data;return(0,r.jsx)("div",{className:"plotly-figure",style:{"overflow-x":"auto"},children:(0,r.jsx)(a,{data:e.data,layout:e.layout})})})},3118(A,e,t){t.r(e),t.d(e,{assets:()=>B,contentTitle:()=>C,default:()=>s,frontMatter:()=>Q,metadata:()=>i,toc:()=>E});const i=JSON.parse('{"id":"tutorials/multiobjective_optimization/index","title":"Multi-Objective Optimization","description":"<LinkButtons","source":"@site/versioned_docs/version-0.5.0/tutorials/multiobjective_optimization/index.mdx","sourceDirName":"tutorials/multiobjective_optimization","slug":"/tutorials/multiobjective_optimization/","permalink":"/docs/0.5.0/tutorials/multiobjective_optimization/","draft":false,"unlisted":false,"tags":[],"version":"0.5.0","lastUpdatedBy":"Cristian Lara","lastUpdatedAt":1746558852000,"frontMatter":{"title":"Multi-Objective Optimization","sidebar_label":"Multi-Objective Optimization"},"sidebar":"tutorials","previous":{"title":"Multi-Task Modeling","permalink":"/docs/0.5.0/tutorials/multi_task/"},"next":{"title":"High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces (SAASBO)","permalink":"/docs/0.5.0/tutorials/saasbo/"}}');var g=t(74848),n=t(28453),r=t(38987),a=t(7877),o=t(1295);const Q={title:"Multi-Objective Optimization",sidebar_label:"Multi-Objective Optimization"},C="Multi-Objective Optimization Ax API",B={},E=[{value:"Using the Service API",id:"using-the-service-api",level:3},{value:"Create an Evaluation Function",id:"create-an-evaluation-function",level:3},{value:"Run Optimization",id:"run-optimization",level:3},{value:"Plot Pareto Frontier",id:"plot-pareto-frontier",level:3},{value:"Problem Statement",id:"problem-statement",level:3},{value:"Pareto Optimality",id:"pareto-optimality",level:3},{value:"Evaluating the Quality of a Pareto Front (Hypervolume)",id:"evaluating-the-quality-of-a-pareto-front-hypervolume",level:3},{value:"Set Objective Thresholds to focus candidate generation in a region of interest",id:"set-objective-thresholds-to-focus-candidate-generation-in-a-region-of-interest",level:3},{value:"Further Information",id:"further-information",level:3},{value:"Setup",id:"setup",level:2},{value:"Define experiment configurations",id:"define-experiment-configurations",level:2},{value:"Search Space",id:"search-space",level:3},{value:"MultiObjectiveOptimizationConfig",id:"multiobjectiveoptimizationconfig",level:3},{value:"Define experiment creation utilities",id:"define-experiment-creation-utilities",level:2},{value:"qNEHVI",id:"qnehvi",level:2},{value:"Plot qNEHVI Pareto Frontier based on model posterior",id:"plot-qnehvi-pareto-frontier-based-on-model-posterior",level:2},{value:"qNParEGO",id:"qnparego",level:2},{value:"Plot qNParEGO Pareto Frontier based on model posterior",id:"plot-qnparego-pareto-frontier-based-on-model-posterior",level:2},{value:"Plot empirical data",id:"plot-empirical-data",level:2},{value:"Plot observed hypervolume, with color representing the iteration that a point was generated on.",id:"plot-observed-hypervolume-with-color-representing-the-iteration-that-a-point-was-generated-on",level:4},{value:"Plot the results",id:"plot-the-results",level:4}];function I(A){const e={a:"a",annotation:"annotation",code:"code",em:"em",h1:"h1",h2:"h2",h3:"h3",h4:"h4",header:"header",img:"img",math:"math",mi:"mi",mn:"mn",mo:"mo",mrow:"mrow",msub:"msub",msubsup:"msubsup",msup:"msup",p:"p",pre:"pre",semantics:"semantics",span:"span",...(0,n.R)(),...A.components};return(0,g.jsxs)(g.Fragment,{children:[(0,g.jsx)(r.A,{githubUrl:"https://github.com/facebook/ax/blob/0.5.0/tutorials/multiobjective_optimization/multiobjective_optimization.ipynb",colabUrl:"https://colab.research.google.com/github/facebook/ax/blob/0.5.0
1/tutorials/multiobjective_optimization/multiobjective_optimization.ipynb"}),"\n",(0,g.jsx)(e.header,{children:(0,g.jsx)(e.h1,{id:"multi-objective-optimization-ax-api",children:"Multi-Objective Optimization Ax API"})}),"\n",(0,g.jsx)(e.h3,{id:"using-the-service-api",children:"Using the Service API"}),"\n",(0,g.jsxs)(e.p,{children:["For Multi-objective optimization (MOO) in the ",(0,g.jsx)(e.code,{children:"AxClient"}),", objectives are specified\nthrough the ",(0,g.jsx)(e.code,{children:"ObjectiveProperties"})," dataclass. An ",(0,g.jsx)(e.code,{children:"ObjectiveProperties"})," requires a boolean\n",(0,g.jsx)(e.code,{children:"minimize"}),", and also accepts an optional floating point ",(0,g.jsx)(e.code,{children:"threshold"}),". If a ",(0,g.jsx)(e.code,{children:"threshold"})," is\nnot specified, Ax will infer it through the use of heuristics. If the user knows the\nregion of interest (because they have specs or prior knowledge), then specifying the\nthresholds is preferable to inferring it. But if the user would need to guess, inferring\nis preferable."]}),"\n",(0,g.jsxs)(e.p,{children:["To learn more about how to choose a threshold, see\n",(0,g.jsx)(e.a,{href:"/docs/0.5.0/tutorials/multiobjective_optimization/#set-objective-thresholds-to-focus-candidate-generation-in-a-region-of-interest",children:"Set Objective Thresholds to focus candidate generation in a region of interest"}),".\nSee the ",(0,g.jsx)(e.a,{href:"/docs/0.5.0/tutorials/gpei_hartmann_service/",children:"Service API Tutorial"})," for more\ninfomation on running experiments with the Service API."]}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"import sys\nin_colab = 'google.colab' in sys.modules\nif in_colab:\n %pip install ax-platform\n"})}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'import torch\nfrom ax.plot.pareto_frontier import plot_pareto_frontier\nfrom ax.plot.pareto_utils import compute_posterior_pareto_frontier\nfrom ax.service.ax_client import AxClient\nfrom ax.service.utils.instantiation import ObjectiveProperties\n\n# Plotting imports and initialization\nfrom ax.utils.notebook.plotting import init_notebook_plotting, render\nfrom botorch.test_functions.multi_objective import BraninCurrin\nimport plotly.io as pio\n\ninit_notebook_plotting()\nif in_colab:\n pio.renderers.default = "colab"\n'})}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.utils.notebook.plotting: Please see\n (https://ax.dev/tutorials/visualizations.html#Fix-for-plots-that-are-not-rendering)\n if visualizations are not rendering."}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'# Load our sample 2-objective problem\nbranin_currin = BraninCurrin(negate=True).to(\n dtype=torch.double,\n device=torch.device("cuda" if torch.cuda.is_available() else "cpu"),\n)\n'})}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'ax_client = AxClient()\nax_client.create_experiment(\n name="moo_experiment",\n parameters=[\n {\n "name": f"x{i+1}",\n "type": "range",\n "bounds": [0.0, 1.0],\n }\n for i in range(2)\n ],\n objectives={\n # `threshold` arguments are optional\n "a": ObjectiveProperties(minimize=False, threshold=branin_currin.ref_point[0]),\n "b": ObjectiveProperties(minimize=False, threshold=branin_currin.ref_point[1]),\n },\n overwrite_existing_experiment=True,\n is_test=True,\n)\n'})}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.service.ax_client: Starting optimization with verbose logging. To disable logging, set the verbose_logging argument to False. Note that float values in the logs are rounded to 6 decimal points."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.service.utils.instantiation: Created search space: SearchSpace(parameters=[RangeParameter(name='x1', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x2', parameter_type=FLOAT, range=[0.0, 1.0])], parameter_constraints=[])."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.core.experiment: The is_test flag has been set to True. This flag is meant purely for development and integration testing purposes. If you are running a live experiment, please set this flag to False"}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.modelbridge.dispatch_utils: Using Models.BOTORCH_MODULAR
1since there is at least one ordered parameter and there are no unordered categorical parameters."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.modelbridge.dispatch_utils: Calculating the number of remaining initialization trials based on num_initialization_trials=None max_initialization_trials=None num_tunable_parameters=2 num_trials=None use_batch_trials=False"}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=5"}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=5"}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.modelbridge.dispatch_utils: verbose, disable_progbar, and jit_compile are not yet supported when using choose_generation_strategy with ModularBoTorchModel, dropping these arguments."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:09] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+BoTorch', steps=[Sobol for 5 trials, BoTorch for subsequent trials]). Iterations after 5 will take longer to generate due to model-fitting."}),"\n",(0,g.jsx)(e.h3,{id:"create-an-evaluation-function",children:"Create an Evaluation Function"}),"\n",(0,g.jsxs)(e.p,{children:["In the case of MOO experiments, evaluation functions can be any arbitrary function that\ntakes in a ",(0,g.jsx)(e.code,{children:"dict"})," of parameter names mapped to values and returns a ",(0,g.jsx)(e.code,{children:"dict"})," of objective\nnames mapped to a ",(0,g.jsx)(e.code,{children:"tuple"})," of mean and SEM values."]}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'def evaluate(parameters):\n evaluation = branin_currin(\n torch.tensor([parameters.get("x1"), parameters.get("x2")])\n )\n # In our case, standard error is 0, since we are computing a synthetic function.\n # Set standard error to None if the noise level is unknown.\n return {"a": (evaluation[0].item(), 0.0), "b": (evaluation[1].item(), 0.0)}\n'})}),"\n",(0,g.jsx)(e.h3,{id:"run-optimization",children:"Run Optimization"}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"for i in range(25):\n parameters, trial_index = ax_client.get_next_trial()\n # Local evaluation here can be replaced with deployment to external system.\n ax_client.complete_trial(trial_index=trial_index, raw_data=evaluate(parameters))\n"})}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/modelbridge/cross_validation.py:439: UserWarning:\nEncountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n[INFO 02-03 18:54:10] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.639492, 'x2': 0.556009} using model Sobol."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:10] ax.service.ax_client: Completed trial 0 with data: {'a': (-56.800846, 0.0), 'b': (-6.504035, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/modelbridge/cross_validation.py:439: UserWarning:\nEncountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n[INFO 02-03 18:54:10] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.22491, 'x2': 0.223322} using model Sobol."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:10] ax.service.ax_client: Completed trial 1 with data: {'a': (-40.606293, 0.0), 'b': (-12.322504, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/modelbridge/cross_validation.py:439: UserWarning:\nEncountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n[INFO 02-03 18:54:10] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.300066, 'x2': 0.960166} using model Sobol."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:10] ax.service.ax_client: Completed trial 2 with data: {'a': (-75.828926, 0.0), 'b': (-5.42404, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/modelbridge/cross_validation.py:439: UserWarning:\nEncountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n[INFO 02-03 18:54:10] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.839709, 'x2': 0.260504} using model Sobol."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:10] ax.service.ax_client: Completed trial 3 with data: {'a': (-18.921333, 0.0), 'b': (-8.860395, 0.0
1)}."}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/modelbridge/cross_validation.py:439: UserWarning:\nEncountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n[INFO 02-03 18:54:10] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.941101, 'x2': 0.809305} using model Sobol."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:10] ax.service.ax_client: Completed trial 4 with data: {'a': (-99.10479, 0.0), 'b': (-4.716988, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:11] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 1.0, 'x2': 0.443529} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:11] ax.service.ax_client: Completed trial 5 with data: {'a': (-15.265464, 0.0), 'b': (-6.882358, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:12] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.81839, 'x2': 1.0} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:12] ax.service.ax_client: Completed trial 6 with data: {'a': (-204.06517, 0.0), 'b': (-4.102039, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:13] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.90544, 'x2': 0.600836} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:13] ax.service.ax_client: Completed trial 7 with data: {'a': (-54.835285, 0.0), 'b': (-5.806404, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:15] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.450589, 'x2': 0.763866} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:15] ax.service.ax_client: Completed trial 8 with data: {'a': (-69.947433, 0.0), 'b': (-5.797382, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:16] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.0, 'x2': 0.753291} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:16] ax.service.ax_client: Completed trial 9 with data: {'a': (-47.392197, 0.0), 'b': (-1.455256, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:17] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 1.0, 'x2': 0.0} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:17] ax.service.ax_client: Completed trial 10 with data: {'a': (-10.960894, 0.0), 'b': (-10.179487, 0.0
1)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:19] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.187868, 'x2': 0.60096} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:19] ax.service.ax_client: Completed trial 11 with data: {'a': (-5.642111, 0.0), 'b': (-7.740734, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:20] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.0, 'x2': 0.493925} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:20] ax.service.ax_client: Completed trial 12 with data: {'a': (-108.342644, 0.0), 'b': (-1.909854, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:21] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.024994, 'x2': 1.0} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:21] ax.service.ax_client: Completed trial 13 with data: {'a': (-10.42739, 0.0), 'b': (-2.187852, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:22] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.088597, 'x2': 0.916316} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:22] ax.service.ax_client: Completed trial 14 with data: {'a': (-1.738521, 0.0), 'b': (-4.522746, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:24] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.053405, 'x2': 0.963678} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:24] ax.service.ax_client: Completed trial 15 with data: {'a': (-5.538787, 0.0), 'b': (-3.317845, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:26] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.008754, 'x2': 1.0} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:26] ax.service.ax_client: Completed trial 16 with data: {'a': (-14.77444, 0.0), 'b': (-1.53793, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:28] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.071137, 'x2': 1.0} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:28] ax.service.ax_client: Completed trial 17 with data: {'a': (-3.801824, 0.0), 'b': (-3.775479, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:31] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.039145, 'x2': 1.0} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:31] ax.service.ax_client: Completed trial 18 with data: {'a': (-7.456717, 0.0), 'b': (-2.724951, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:33] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.109206, 'x2': 0.870326} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:33] ax.service.ax_client: Completed trial 19 with data: {'a': (-0.689599, 0.0), 'b': (-5.174188, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:36] ax.service.ax_client: Generated new trial 20 with parameters {'x1': 0.077207, 'x2': 0.952719} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:36] ax.service.ax_client: Completed trial 20 with data: {'a': (-2.730387, 0.0), 'b': (-4.092929, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:39] ax.service.ax_client: Generated new trial 21 with parameters {'x1': 0.016634, 'x2': 1.0} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:39] ax.service.ax_client: Completed trial 21 with data: {'a': (-12.544319, 0.0), 'b': (-1.85649, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:41] ax.service.ax_client: Generated new trial 22 with parameters {'x1': 0.553087, 'x2': 0.0} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:41] ax.service.ax_client: Completed trial 22 with data: {'a': (-5.167106, 0.0), 'b': (-11.387817, 0.0)}."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:44] ax.service.ax_client: Generated new trial 23 with parameters {'x1': 0.031798, 'x2': 1.0} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:44] ax.service.ax_client: Completed trial 23 with data: {'a': (-8.900707, 0.0), 'b': (-2.450435, 0.0
1)}."}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/botorch/optim/optimize.py:652: RuntimeWarning:\nOptimization failed in gen_candidates_scipy with the following warning(s):\n[NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), OptimizationWarning('Optimization failed within scipy.optimize.minimize with status 2 and message ABNORMAL: .'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal')]\nTrying again with a new set of initial conditions."}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal\n[INFO 02-03 18:54:52] ax.service.ax_client: Generated new trial 24 with parameters {'x1': 0.047113, 'x2': 1.0} using model BoTorch."}),"\n",(0,g.jsx)(a.A,{children:"[INFO 02-03 18:54:52] ax.service.ax_client: Completed trial 24 with data: {'a': (-6.138559, 0.0), 'b': (-3.010158, 0.0)}."}),"\n",(0,g.jsx)(e.h3,{id:"plot-pareto-frontier",children:"Plot Pareto Frontier"}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'objectives = ax_client.experiment.optimization_config.objective.objectives\nfrontier = compute_posterior_pareto_frontier(\n experiment=ax_client.experiment,\n data=ax_client.experiment.fetch_data(),\n primary_objective=objectives[1].metric,\n secondary_objective=objectives[0].metric,\n absolute_metrics=["a", "b"],\n num_points=20,\n)\nrender(plot_pareto_frontier(frontier, CI_level=0.90))\n'})}),"\n",(0,g.jsx)(o.z,{data:t(6029)}),"\n",(0,g.jsx)(e.h1,{id:"deep-dive",children:"Deep Dive"}),"\n",(0,g.jsx)(e.p,{children:"In the rest of this tutorial, we will show two algorithms available in Ax for\nmulti-objective optimization and visualize how they compare to eachother and to\nquasirandom search."}),"\n",(0,g.jsxs)(e.p,{children:["MOO covers the case where we care about multiple outcomes in our experiment but we do\nnot know before hand a specific weighting of those objectives (covered by\n",(0,g.jsx)(e.code,{children:"ScalarizedObjective"}),") or a specific constraint on one objective (covered by\n",(0,g.jsx)(e.code,{children:"OutcomeConstraint"}),"s) that will produce the best result."]}),"\n",(0,g.jsx)(e.p,{children:"The solution in this case is to find a whole Pareto frontier, a surface in outcome-space\ncontaining points that can't be improved on in every outcome. This shows us the\ntradeoffs between objectives that we can choose to make."}),"\n",(0,g.jsx)(e.h3,{id:"problem-statement",children:"Problem Statement"}),"\n",(0,g.jsxs)(e.p,{children:["Optimize a list of M objective functions ",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsxs)(e.mrow,{children:[(0,g.jsx)(e.mo,{fence:"true",stretchy:"true",minsize:"1.2em",maxsize:"1.2em",children:"("}),(0,g.jsxs)(e.msup,{children:[(0,g.jsx)(e.mi,{children:"f"}),(0,g.jsxs)(e.mrow,{children:[(0,g.jsx)(e.mo,{stretchy:"false",children:"("}),(0,g.jsx)(e.mn,{children:"1"}),(0,g.jsx)(e.mo,{stretchy:"false",children:")"})]})]}),(0,g.jsx)(e.mo,{stretchy:"false",children:"("}),(0,g.jsx)(e.mi,{children:"x"}),(0,g.jsx)(e.mo,{stretchy:"false",children:")"}),(0,g.jsx)(e.mo,{separator:"true",children:","}),(0,g.jsx)(e.mi,{mathvariant:"normal",children:"."}),(0,g.jsx)(e.mi,{mathvariant:"normal",children:"."}),(0,g.jsx)(e.mi,{mathvariant:"normal",children:"."}),(0,g.jsx)(e.mo,{separator:"true",children:","}),(0,g.jsxs)(e.msup,{children:[(0,g.jsx)(e.mi,{children:"f"}),(0,g.jsxs)(e.mrow,{children:[(0,g.jsx)(e.mo,{stretchy:"false",children:"("}),(0,g.jsx)(e.mi,{children:"M"}),(0,g.jsx)(e.mo,{stretchy:"false",children:")"})]})]}),(0,g.jsx)(e.mo,{stretchy:"false",children:"("}),(0,g.jsx)(e.mi,{children:"x"}),(0,g.jsx)(e.mo,{stretchy:"false",children:")"}),(0,g.jsx)(e.mo,{fence:"true",stretchy:"true",minsize:"1.2em",maxsize:"1.2em",children:")"})]}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:" \\bigl(f^{(1)}( x),..., f^{(M)}( x) \\bigr)"})]})})}),(0,g.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"1.238em",verticalAlign:"-0.35em"}}
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",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsxs)(e.mrow,{children:[(0,g.jsx)(e.mi,{mathvariant:"script",children:"X"}),(0,g.jsx)(e.mo,{children:"\u2282"}),(0,g.jsxs)(e.msup,{children:[(0,g.jsx)(e.mi,{mathvariant:"double-struck",children:"R"}),(0,g.jsx)(e.mi,{children:"d"})]})]}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\mathcal X \\subset \\mathbb R^d"})]})})}),(0,g.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"0.7224em",verticalAlign:"-0.0391em"}}),(0,g.jsx)(e.span,{className:"mord 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1,children:(0,g.jsxs)(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[(0,g.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,g.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,g.jsxs)(e.span,{className:"mord mtight",children:[(0,g.jsx)(e.span,{className:"mopen mtight",children:"("}),(0,g.jsx)(e.span,{className:"mord mathnormal mtight",children:"i"}),(0,g.jsx)(e.span,{className:"mclose mtight",children:")"})]})})]})})})})})]})]})})]})," are expensive-to-evaluate black-box functions with no known\nanalytical expression, and no observed gradients. For instance, a machine learning model\nwhere we're interested in maximizing accuracy and minimizing inference time, with\n",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsx)(e.mrow,{children:(0,g.jsx)(e.mi,{mathvariant:"script",children:"X"})}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\mathcal X"})]})})}),(0,g.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,g.jsx)(e.span,{className:"mord mathcal",style:{marginRight:"0.1464em"},children:"X"})]})})]})," the set of possible configuration spaces"]}),"\n",(0,g.jsx)(e.h3,{id:"pareto-optimality",children:"Pareto Optimality"}),"\n",(0,g.jsxs)(e.p,{children:["In a multi-objective optimization problem, there typically is no single best solution.\nRather, the ",(0,g.jsx)(e.em,{children:"goal"})," is to identify the set of Pareto optimal solutions such that any\nimprovement in one objective means deteriorating another. Provided with the Pareto set,\ndecision-makers can select an objective trade-off according to their preferences. In the\nplot below, the red dots are the Pareto optimal solutions (assuming both objectives are\nto be minimized).\n",(0,g.jsx)(e.img,{src:"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAE5wAABCzCAIAAACj6tz9AAAABGdBTUEAALGPC/xhBQAADGVpQ0NQSUNDIFByb2ZpbGUAAEiJlZcHXJNHG8DvHZkkrEAEZIS9RJEZQEYIK4KATEFUQhJIGDEmBBUXoqUK1i2iOCpaFVCwDkDqQMQ6i+K2juJApVKLVVyofBcS0Npv/L7jd+/93+eee+55Hu7y3gGg08mXyXJRXQDypPnyuPBg1qSUVBbpESDAP20AAIUvUMg4sbFRkMFQ+/fy+jpAVO0VF5Wtf/b/16IvFCkEACBpkDOECkEe5BYA8GKBTJ4PADEEyq1n5stULIZsIIcOQp6r4iw1r1Rxhpp3DOokxHEhNwFApvH58iwAtNugnFUgyIJ2tB9BdpUKJVIAdAwgBwjEfCHkBMij8vKmq7gIsgPUl0HeDZmd8YXNrL/Zzxi2z+dnDbM6rsFCDpEoZLn82f9nav53yctVDs1hBytNLI+IU8UPc3gzZ3qkimmQe6QZ0TGqXEN+KxGq8w4AShUrIxLV+qipQMGF+QNMyK5CfkgkZFPIYdLc6CiNPCNTEsaDDFcLOkuSz0vQjF0iUoTGa2xukk+PixniTDmXoxlbx5cPzqvSb1PmJHI09m+KRbwh+68KxQnJkKkAYNQCSVI0ZLgGMQNFTnykWgezKhRzo4d05Mo4lf82kNkiaXiw2j6WlikPi9Poy/IUQ/FiJWIJL1rDFfnihAh1frAaAX/QfyPIDSIpJ3HIjkgxKWooFqEoJFQdO9YukiZq4sXuyfKD4zRje2W5sRp9nCzKDVfJrSCbKAriNWPxcflwcart41Gy/NgEtZ94ejZ/fKzaH7wARAEuCAEsoIQ1A0wH2UDS3tPYA9/UPWGAD+QgC4iAi0YyNCJ5sEcKn/GgEPwBSQQUw+OCB3tFoADKPw5L1U8XkDnYWzA4Igc8hpwHIkEufFcOjpIOz5YEHkGJ5B+zC6CvubCq+v4p40BJlEaiHLLL0hnSJIYSQ4gRxDCiI26CB+B+eBR8BsHqhrNxnyFvP+sTHhM6CA8I1widhFvTJMXyr3yZADqh/TBNxBlfRozbQZueeDDuD61DyzgTNwEuuAech4MHwpk9oZSr8VsVO+vfxDkcwRc51+hRXCkoZQQliOLw9UhtJ23PYSuqjH6ZH7WvGcNZ5Q73fD0/94s8C2Eb+bUmtgQ7gJ3GTmBnsSNYI2Bhx7Em7AJ2VMXDa+jR4Boami1u0J8caEfyj/n4mjlVmVS41rp2u37Q9IF80ax81QbjTpfNlkuyxPksDvwKiFg8qWD0KJabq5srAKpvivpn6iVz8FuBMM99lhXfBcA/ZWBg4MhnWRTcpwefwm3e81lmXwsA/RgAZ74RKOUFahmuehDgr4EO3FHGwBxYAwcYkRvwAn4gCISC8SAGJIAUMBXmWQzXsxzMBHPBQlACysBKsA5sBFvBdrAb7AX7QSM4Ak6An8F5cAlcA7fh+ukCz0AveA36EQQhIXSEgRgjFogt4oy4IWwkAAlFopA4JAVJR7IQKaJE5iKLkDJkNbIR2YZUIz8ih5ETyFmkA7mF3Ee6kb+Q9yiG0lAD1Ay1Q8egbJSDRqIJ6BQ0C52BFqKL0eVoBVqF7kEb0BPoefQa2ok+Q/swgGlhTMwSc8HYGBeLwVKxTEyOzcdKsXKsCqvDmuF/+grWifVg73AizsBZuAtcwxF4Ii7AZ+Dz8WX4Rnw33oC34Vfw+3gv/olAJ5gSnAm+BB5hEiGLMJNQQign7CQcIpyCu6mL8JpIJDKJ9kRvuBtTiNnEOcRlxM3EemILsYP4kNhHIpGMSc4kf1IMiU/KJ5WQNpD2kI6TLpO6SG/JWmQLshs5jJxKlpKLyeXkGvIx8mXyE3I/RZdiS/GlxFCElNmUFZQdlGbKRUoXpZ+qR7Wn+lMTqNnUhdQKah31FPUO9aWWlpaVlo/WRC2JVpFWhdY+rTNa97Xe0fRpTjQuLY2mpC2n7aK10G7RXtLpdDt6ED2Vnk9fTq+mn6Tfo7/VZmiP1uZpC7UXaFdqN2hf1n6uQ9Gx1eHoTNUp1CnXOaBzUadHl6Jrp8vV5evO163UPax7Q7dPj6E3Vi9GL09vmV6N3lm9p/okfTv9UH2h/mL97fon9R8yMIY1g8sQMBYxdjBOMboMiAb2BjyDbIMyg70G7Qa9hvqGHoZJhrMMKw2PGnYyMaYdk8fMZa5g7mdeZ74fYTaCM0I0YumIuhGXR7wxGmkUZCQyKjWqN7pm9N6YZRxqnGO8yrjR+K4JbuJkMtFkpskWk1MmPSMNRvqNFIwsHbl/5K+mqKmTaZzpHNPtphdM+8zMzcLNZGYbzE6a9ZgzzYPMs83Xmh8z77ZgWARYSCzWWhy3+J1lyOKwclkVrDZWr6WpZYSl0nKbZbtlv5W9VaJVsVW91V1rqjXbOtN6rXWrda+Nhc0Em7k2tTa/2lJs2bZi2/W2p23f2NnbJdt9a9do99TeyJ5nX2hfa3/Hge4Q6DDDocrhqiPRke2Y47jZ8ZIT6uTpJHaqdLrojDp7OUucNzt3jCKM8hklHVU16oYLzYXjUuBS63J/NHN01Oji0Y2jn4+xGZM6ZtWY02M+uXq65rrucL09Vn/s+LHFY5vH/uXm5CZwq3S76k53D3Nf4N7k/sLD2UPkscXjpifDc4Lnt56tnh+9vL3kXnVe3d423unem7xvsA3Ysexl7DM+BJ9gnwU+R3ze+Xr55vvu9/3Tz8Uvx6/G7+k4+3GicTvGPfS38uf7b/PvDGAFpAd8H9AZaBnID6wKfBBkHSQM2hn0hOPIyebs4TwPdg2WBx8KfsP15c7jtoRgIeEhpSHtofqhiaEbQ++FWYVlhdWG9YZ7hs8Jb4kgRERGrIq4wTPjCXjVvN7x3uPnjW+LpEXGR26MfBDlFCWPap6AThg/Yc2EO9G20dLoxhgQw4tZE3M31j52RuxPE4kTYydWTnwcNzZubtzpeEb8tPia+NcJwQkrEm4nOiQqE1uTdJLSkqqT3iSHJK9O7pw0ZtK8SedTTFIkKU2ppNSk1J2pfZNDJ6+b3JXmmVaSdn2K/ZRZU85ONZmaO/XoNJ1p/GkH0gnpyek16R/4Mfwqfl8GL2NTRq+AK1gveCYMEq4Vdov8RatFTzL9M1dnPs3
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front"})]}),"\n",(0,g.jsx)(e.h3,{id:"evaluating-the-quality-of-a-pareto-front-hypervolume",children:"Evaluating the Quality of a Pareto Front (Hypervolume)"}),"\n",(0,g.jsxs)(e.p,{children:["Given a reference point ",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsxs)(e.mrow,{children:[(0,g.jsx)(e.mi,{children:"r"}),(0,g.jsx)(e.mo,{children:"\u2208"}),(0,g.jsxs)(e.msup,{children:[(0,g.jsx)(e.mi,{mathvariant:"double-struck",children:"R"}),(0,g.jsx)(e.mi,{children:"M"})]})]}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:" r \\in \\mathbb R^M"})]})})}),(0,g.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"0.5782em",verticalAlign:"-0.0391em"}}),(0,g.jsx)(e.span,{className:"mord 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1,children:(0,g.jsxs)(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[(0,g.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,g.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,g.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.109em"},children:"M"})})]})})})})})]})]})]})]}),", which we represent as a list of M\n",(0,g.jsx)(e.code,{children:"ObjectiveThreshold"}),"s, one for each coordinate, the hypervolume (HV) of a Pareto set\n",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsxs)(e.mrow,{children:[(0,g.jsx)(e.mi,{mathvariant:"script",children:"P"}),(0,g.jsx)(e.mo,{children:"="}),(0,g.jsxs)(e.msubsup,{children:[(0,g.jsxs)(e.mrow,{children:[(0,g.jsx)(e.mi,{children:"f"}),(0,g.jsx)(e.mo,{stretchy:"false",children:"("}),(0,g.jsxs)(e.msub,{children:[(0,g.jsx)(e.mi,{children:"x"}),(0,g.jsx)(e.mi,{children:"i"})]}),(0,g.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,g.jsxs)(e.mrow,{children:[(0,g.jsx)(e.mi,{children:"i"}),(0,g.jsx)(e.mo,{children:"="}),(0,g.jsx)(e.mn,{children:"1"})]}),(0,g.jsxs)(e.mrow,{children:[(0,g.jsx)(e.mi,{mathvariant:"normal",children:"\u2223"}),(0,g.jsx)(e.mi,{mathvariant:"script",children:"P"}),(0,g.jsx)(e.mi,{mathvariant:"normal",children:"\u2223"})]})]})]}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\mathcal P = { f(x_i)}_{i=1}^{|\\mathcal P|}"})]})})}),(0,g.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,g.jsx)(e.span,{className:"mord mathcal",style:{marginRight:"0.0822em"},children:"P"}),(0,g.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,g.jsx)(e.span,{className:"mrel",children:"="}),(0,g.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"1.3276em",verticalAlign:"-0.2997em"}}),(0,g.jsxs)(e.span,{className:"mord",children:[(0,g.jsxs)(e.span,{className:"mord",children:[(0,g.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.1076em"},children:"f"}),(0,g.jsx)(e.span,{className:"mopen",children:"("}),(0,g.jsxs)(e.span,{className:"mord",children:[(0,g.jsx)(e.span,{className:"mord 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The reference point should be set to be slightly worse (10% is reasonable)\nthan the worst value of each objective that a decision maker would tolerate. In the\nfigure below, the grey area is the hypervolume in this 2-objective problem.\n",(0,g.jsx)(e.img,{src:"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAEo0AABAwCAIAAAAyLI+dAAAABGdBTUEAALGPC/xhBQAADGVpQ0NQSUNDIFByb2ZpbGUAAEiJlZcHXJNHG8DvHZkkrEAEZIS9RJEZQEYIK4KATEFUQhJIGDEmBBUXoqUK1i2iOCpaFVCwDkDqQMQ6i+K2juJApVKLVVyofBcS0Npv/L7jd+/93+eee+55Hu7y3gGg08mXyXJRXQDypPnyuPBg1qSUVBbpESDAP20AAIUvUMg4sbFRkMFQ+/fy+jpAVO0VF5Wtf/b/16IvFCkEACBpkDOECkEe5BYA8GKBTJ4PADEEyq1n5stULIZsIIcOQp6r4iw1r1Rxhpp3DOokxHEhNwFApvH58iwAtNugnFUgyIJ2tB9BdpUKJV
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1with a very strict pair of thresholds, (-18, -2). Only\nthe white region in the upper right exceeds both thresholds. Many points do not lie in\nthe dominating region, but there are still more focused there than in the second\nexamples.\n",(0,g.jsx)(e.img,{src:"data:image/png;base64,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
1aHVapQx/reTxl3/9fmzubcbqzmopyb8Ui6Us/2xrpmTzN145bxMQIECAAAECBAgQIECAAAECBAgQIECAAAECBAi8voATI7++mVcQIEBgrAV2ujtx88k3cW/7Xgnj9yIT8TOony2z8jNrv9vvxkZnM25t3IlvNu/ETnd3rE0sHAECBAgQIECAAAECBAgQIECAAAECBAgQIEDgJAUE9k9S33sTIEBgCAX2+nux1nkSGyUrPzP0X9Qyaz+D+znd6vbj2Ot1XzSZxwgQIECAAAECBAgQIECAAAECBAgQIECAAAECBA5BQGD/EBDNggABAuMkkEH7Tq8T3RKszwz9/Pd8ywz+vOzsbVdl+XslyK8RIECAAAECBAgQIECAAAECBAgQIECAAAECBAgcjUDzaGZrrgQIECAwqgIZsG/WmtGoNaqM/Rdl7WfwP/9NNadjtjlTlecf1eXVbwIECBAgQIAAAQIECBAgQIAAAQIECBAgQIDAsAvI2B/2EdI/AgQIHLNAvQT0Z5uzMdWY+t53rtfqMd+ai6WphWjWHSf2vVieJECAAAECBAgQIECAAAECBAgQIECAAAECBAi8hYDA/lvgeSkBAgTGUWCmMR3XFq/Ghdlz0YjyZ6Jf/isZ+tkyS7/X70Wr3ipB/YW4WKbJ6drlvkaAAAECBAgQIECAAAECBAgQIECAAAECBAgQIHA0AlIsj8bVXAkQIDCyAu1GK87PrsSjqYexVP6VOvtRb9aroH4talWJ/qWppViZPlumOxeL7YWolex9jQABAgQIECBAgAABAgQIECBAgAABAgQIECBA4GgEBPaPxtVcCRAgMLICWVZ/qb0Y59vn4lrtSnRa3ehO96LT65RM/WbMt+fj6vzleKdk9c+VUvxZkj9KwF8jQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBA4GgGB/aNxNVcCBAiMrEBm5TfrjZiuTcVCzMf83HzMnpmLbq8XjXo9ppvTcXp6uQr+N2qNspyC+iM72DpOgAABAgQIECBAgAABAgQIECBAgAABAgQIjISAwP5IDJNOEiBA4PgFGlGC+LV2XJ27HFdXrh5/B7wjAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAJeCkyD4IBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIEBgiAUE9od4cHSNAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgI7PsMECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgACBIRYQ2B/iwdE1AgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECAgsO8zQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIEhlhAYH+IB0fXCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQICAwL7PAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQGGIBgf0hHhxdI0CAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECAvs+AwQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAYIgFBPaHeHB0jQABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQINBEQIECAAAECBCZFoNftRWd3LzaebEav2496ox4z89MxPdOOWq32HcPjra14tLkZq5tbsbm7G/1+P9rNZsy0W3F+YTFOz81GvUy//zXfvdgNAgQIECBAgAABAgQIECBAgAABAgQIECBwyAIC+4cManYECBAgQIDA8AlkYL7X68fudifWVzfi9o37sdfpRrME6lcunYrGykI0SuC+Vq9VQfz76+vxyZ07cf3e/bj3ZL167fz0VJxdmI+/uno15srrplqtaOw7GGD4llqPCBAgQIAAAQIECBAgQIAAAQIECBAgQGBcBAT2x2UkLQcBAgQIECDwUoHVB0/i7s2H8fnHN+KbL+7G43K/W7L3G41GLJ9diPNXTseP/837MX1mLu5ub8Snd+/Gp7fvxJOdndje7US/zHlzd6dk8G/GbmevCvb//OqVOLe48NL39AQBAgQIECBAgAABAgQIECBAgAABAgQIEDgsAYH9w5I0HwIECBAgQGDoBDJTv/wX9289io//vz/G7359PW58fjt2NneqLPx6rZTiX5iOc5dOR7NVSu1fW4qvehtx/cGD+OL+/arUfim4Xy3XZjWvfmyVQP/Gzm5cPrUcS7Mz0S4HByjJP3RDr0MECBAgQIAAAQIECBAgQIAAAQIECBAYKwGB/bEaTgtDgAABAgQI7BfI8vud3b24cf1O/OYffh9rj9ajW0rw1+v1cnk6ZWenEw/urMa//OqTaN5ciMdX2rHW3Y0M+u9vg+D91u5uPNxYjztra3Fmfi7Ozs9HU0n+/VRuEyBAgAABAgQIECBAgAABAgQIECBAgMAhCwjsHzKo2REgQIAAAQLDI7C7XYLwd9dKGf4H1aVfAv2ZxT8I0mdP87Gdrd24daNk6Nd3orO4FJ3Wi5chX7fX61VZ+w83NuPx1lacnpt78cQeJUCAAAECBAgQIECAAAECBAgQIECAAAEChyQgsH9IkGZDgAABAgQIDJ/A5vp23Cyl9+/fflQF7xvNzNR/NhM/e52Z/etb2xHrjYid2YhSXv+lrRwYsNfrxtr2VjzZ3i6v7X3/9C+dkScIECBAgAABAgQIECBAgAABAgQIECBAgMDBBP58z/bBXmcqAgQIECBAgMCICNRKWn75rwTk8/plrZ7x+ahFuwT1G8+V4d//mszab5VpTs3MxtLMTDRecKDA/undJkCAAAECBAgQIECAAAECBAgQIECAAAECbysgsP+2gl5PgAABAgQIDK1Ao9mIqdl2tKaaUW+UzZ4SlH9Ry0czWD/basfCzHRMtV5ciz+PC8hA/kyZ7sz8XBXcr79kni96H48RIECAAAECBAgQIECAAAECBAgQIECAAIE3ERDYfxM1ryFAgAABAgRGQmB2bjquvHc+Vi6djrzdLKX4q8z9fb3P+/V6LRYWZ+PShdPx0ysX48LSwtMpynOD6fM6y+4vTE/HheWlWFlYqA4CENjfh+kmAQIECBAgQIAAAQIECBAgQIAAAQIECByJQPNI5mqmBAgQIECAAIEhEGi1m7F0ZiEuvXMu3vvJlbj3zcNYe7Qe3b1eFbCvyuqXaeYWZuOdH12Oqx9djvNXL8Xs2mr0Snr+k+3t2O50qgr+zZLxP9VsxrXTp+P9lZUqYz/vawQIECBAgAABAgQIECBAgAABAgQIECBA4KgF7I0+amHzJ0CAAAECBE5MoFYy8Ru1elz74cUSyP838Zt/+G388bdfx+b6dvR7UWXqz5eg/sV3z8Vf/e1H8d5HV2J2aSZWNpfj4tJyfHrnTtxeW4tuydRfni3TlUz9D8+dK8H9UzHTbp/YcnljAgQIECBAgAABAgQIECBAgAABAgQIEJgsAYH9yRpvS0uAAIH/v73zfK+jyBJ3KefgnLMNGDB5AMMwaZ/5Mv/kft0P+2l3Z+f3PLs7sMsMQxoYDMZgHLEt5yAr51+9ZcpcS1fylXQl3fAWtPuqu7q66j1d3afPqVNd4QTitOfxv9nZyRgtPRk/hx6/ix6XhoaW0BD/M0lgJQSIyu/b3BMOxoh8ptzfd2RXGHowEq+zudAUp+bv7e8KW7b3J+d/36bu0NzSFLbGfETjd7W1hsGxsXg9zoXO6Mjv7+wIW7u7Q3ecjt8rciXS8BgJSEACEpCABCQgAQlIQAISkIAEJCABCUhAAhJYCQEd+yuh5jESkIAEJFB2AtGdHyOqp6MDdTpMzQzFZTg0N7WHpsb4XfSGrujgj879hqayn9cC64NAZ3d7YNmxd0uYmpwOD6Njf25mNjnxO+L29o62J0DgxGfZ0dvzxHb/kIAEJCABCUhAAhKQgAQkIAEJSEACEpCABCQgAQlsBAEd+xtB3XNKQAISkMATBIjOH5u6GUYnB8LI1LXk2J+eHYtTqLckx35rU3/obj0Y+jqeSc79htD4xPH+IYFSCRC939zcFHp6O+NAkrnAVP38bZKABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkIAEJVDIBHfuVLB3rJgEJSKAOCMzNzYTp2dEwMnE5DE6cDQ/HL8a/R+I3zadilH5jdOy3hdamvjQ1f2tLf2iLTv7mxq46IGMT14pAY1NjaOtoXaviLVcCEpCABCQgAQlIQAISkIAEJCABCUhAAhKQgAQkUHYChjyWHakFSkACEpDAcgjMzE2Eial7YXA8OvXHLiQn/+zcbIzMbwhzsaCZ2ckwPn0vPJw4H+4MfxbGJm8up3
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Information"}),"\n",(0,g.jsx)(e.p,{children:"A deeper explanation of our the qNEHVI [1] and qNParEGO [2] algorithms this notebook\nexplores can be found at"}),"\n",(0,g.jsxs)(e.p,{children:["[1]\n",(0,g.jsx)(e.a,{href:"https://arxiv.org/abs/2105.08195",children:"S. Daulton, M. Balandat, and E. Bakshy. Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement. Advances in Neural Information Processing Systems 34, 2021."})]}),"\n",(0,g.jsxs)(e.p,{children:["[2]\n",(0,g.jsx)(e.a,{href:"https://arxiv.org/abs/2006.05078",children:"S. Daulton, M. Balandat, and E. Bakshy. Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization. Advances in Neural Information Processing Systems 33, 2020."})]}),"\n",(0,g.jsxs)(e.p,{children:["In addition, the underlying BoTorch implementation has a researcher-oriented tutorial at\n",(0,g.jsx)(e.a,{href:"https://botorch.org/tutorials/multi_objective_bo",children:"https://botorch.org/tutorials/multi_objective_bo"}),"."]}),"\n",(0,g.jsx)(e.h2,{id:"setup",children:"Setup"}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"import numpy as np\nimport pandas as pd\nfrom ax.core.data import Data\nfrom ax.core.experiment import Experiment\nfrom ax.core.metric import Metric\nfrom ax.core.objective import MultiObjective, Objective\nfrom ax.core.optimization_config import (\n MultiObjectiveOptimizationConfig,\n ObjectiveThreshold,\n)\n\nfrom ax.core.parameter import ParameterType, RangeParameter\nfrom ax.core.search_space import SearchSpace\nfrom ax.metrics.noisy_function import NoisyFunctionMetric\n\n# Analysis utilities, including a method to evaluate hypervolumes\nfrom ax.modelbridge.modelbridge_utils import observed_hypervolume\nfrom ax.modelbridge.registry import Models\nfrom ax.runners.synthetic import SyntheticRunner\nfrom ax.service.utils.report_utils import exp_to_df\n\n# BoTorch acquisition class for ParEGO\nfrom botor
1ch.acquisition.multi_objective.parego import qLogNParEGO\n"})}),"\n",(0,g.jsx)(e.h2,{id:"define-experiment-configurations",children:"Define experiment configurations"}),"\n",(0,g.jsx)(e.h3,{id:"search-space",children:"Search Space"}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'x1 = RangeParameter(name="x1", lower=0, upper=1, parameter_type=ParameterType.FLOAT)\nx2 = RangeParameter(name="x2", lower=0, upper=1, parameter_type=ParameterType.FLOAT)\n\nsearch_space = SearchSpace(parameters=[x1, x2])\n'})}),"\n",(0,g.jsx)(e.h3,{id:"multiobjectiveoptimizationconfig",children:"MultiObjectiveOptimizationConfig"}),"\n",(0,g.jsxs)(e.p,{children:["To optimize multiple objective we must create a ",(0,g.jsx)(e.code,{children:"MultiObjective"})," containing the metrics\nwe'll optimize and ",(0,g.jsx)(e.code,{children:"MultiObjectiveOptimizationConfig"})," (which contains\n",(0,g.jsx)(e.code,{children:"ObjectiveThreshold"}),"s) instead of our more typical ",(0,g.jsx)(e.code,{children:"Objective"})," and ",(0,g.jsx)(e.code,{children:"OptimizationConfig"})]}),"\n",(0,g.jsxs)(e.p,{children:["We define ",(0,g.jsx)(e.code,{children:"NoisyFunctionMetric"}),"s to wrap our synthetic Branin-Currin problem's outputs.\nAdd noise to see how robust our different optimization algorithms are."]}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'class MetricA(NoisyFunctionMetric):\n def f(self, x: np.ndarray) -> float:\n return float(branin_currin(torch.tensor(x))[0])\n\n\nclass MetricB(NoisyFunctionMetric):\n def f(self, x: np.ndarray) -> float:\n return float(branin_currin(torch.tensor(x))[1])\n\n\nmetric_a = MetricA("a", ["x1", "x2"], noise_sd=0.0, lower_is_better=False)\nmetric_b = MetricB("b", ["x1", "x2"], noise_sd=0.0, lower_is_better=False)\n'})}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"mo = MultiObjective(\n objectives=[Objective(metric=metric_a), Objective(metric=metric_b)],\n)\n"})}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"objective_thresholds = [\n ObjectiveThreshold(metric=metric, bound=val, relative=False)\n for metric, val in zip(mo.metrics, branin_currin.ref_point)\n]\n"})}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"optimization_config = MultiObjectiveOptimizationConfig(\n objective=mo,\n objective_thresholds=objective_thresholds,\n)\n"})}),"\n",(0,g.jsx)(e.h2,{id:"define-experiment-creation-utilities",children:"Define experiment creation utilities"}),"\n",(0,g.jsx)(e.p,{children:"These construct our experiment, then initialize with Sobol points before we fit a\nGaussian Process model to those initial points."}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"# Reasonable defaults for number of quasi-random initialization points and for subsequent model-generated trials.\nN_INIT = 6\nN_BATCH = 25\n"})}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'def build_experiment():\n experiment = Experiment(\n name="pareto_experiment",\n search_space=search_space,\n optimization_config=optimization_config,\n runner=SyntheticRunner(),\n )\n return experiment\n'})}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"## Initialize with Sobol samples\ndef initialize_experiment(experiment):\n sobol = Models.SOBOL(search_space=experiment.search_space, seed=1234)\n for _ in range(N_INIT):\n experiment.new_trial(sobol.gen(1)).run()\n return experiment.fetch_data()\n"})}),"\n",(0,g.jsx)(e.h1,{id:"sobol",children:"Sobol"}),"\n",(0,g.jsx)(e.p,{children:"We use quasirandom points as a fast baseline for evaluating the quality of our\nmulti-objective optimization algorithms."}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"sobol_experiment = build_experiment()\nsobol_data = initialize_experiment(sobol_experiment)\n"})}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'sobol_model = Models.SOBOL(\n experiment=sobol_experiment,\n data=sobol_data,\n)\nsobol_hv_list = []\nfor i in range(N_BATCH):\n generator_run = sobol_model.gen(1)\n trial = sobol_experiment.new_trial(generator_run=generator_run)\n trial.run()\n exp_df = exp_to_df(sobol_experiment)\n outcomes = np.array(exp_df[["a", "b"]], dtype=np.double)\n # Fit a GP-based model in order to calculate hypervolume.\n # We will not use this model to generate new points.\
1n dummy_model = Models.BOTORCH_MODULAR(\n experiment=sobol_experiment,\n data=sobol_experiment.fetch_data(),\n )\n try:\n hv = observed_hypervolume(modelbridge=dummy_model)\n except:\n hv = 0\n print("Failed to compute hv")\n sobol_hv_list.append(hv)\n print(f"Iteration: {i}, HV: {hv}")\n\nsobol_outcomes = np.array(exp_to_df(sobol_experiment)[["a", "b"]], dtype=np.double)\n'})}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 0, HV: 0.0\nIteration: 1, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 2, HV: 0.0\nIteration: 3, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 4, HV: 0.0\nIteration: 5, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 6, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 7, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 8, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 9, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 10, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 11, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 12, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 13, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 14, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 15, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 16, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 17, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 18, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 19, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 20, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 21, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 22, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 23, HV: 28.586963178726865"}),"\n",(0,g.jsx)(a.A,{children:"/home/runner/work/Ax/Ax/ax/core/data.py:295: FutureWarning:\nThe behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 24, HV: 28.586963178726865"}),"\n",(0,g.jsx)(e.h2,{id:"qnehvi",children:"qNEHVI"}),"\n",(0,g.jsx)(e.p,{children:"Noisy Expected Hypervolume Improvement. This is our current recommended algorithm for\nmulti-objective optimization."}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"ehvi_experiment = build_experiment()\nehvi_data = initialize_experiment(ehvi_experiment)\n"})}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'ehvi_hv_list = []\nehvi_model = None\nfor i in range(N_BATCH):\n ehvi_model = Models.BOTORCH_MODULAR(\n experiment=ehvi_experiment,\n data=ehvi_data,\n )\n generator_run = ehvi_model.gen(1)\n trial = ehvi_experiment.new_trial(generator_run=generator_run)\n trial.run()\n ehvi_data = Data.from_multiple_data([ehvi_data, trial.fetch_data()])\n\n exp_df = exp_to_df(ehvi_experiment)\n outcomes = np.array(exp_df[["a", "b"]], dtype=np.double)\n try:\n hv = observed_hypervolume(modelbridge=ehvi_model)\n except:\n hv = 0\n print("Failed to compute hv")\n ehvi_hv_list.append(hv)\n print(f"Iteration: {i}, HV: {hv}")\n\nehvi_outcomes = np.array(exp_to_df(ehvi_experiment)[["a", "b"]], dtype=np.double)\n'})}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 0, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 1, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 2, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 3, HV: 2.369795709893773"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 4, HV: 2.369795709893773"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 5, HV: 32.94757671976549"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 6, HV: 44.25430688748453"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 7, HV: 46.11925211936741"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 8, HV: 46.11925211936741"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 9, HV: 49.18007420754867"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 10, HV: 51.212207136398376"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 11, HV: 52.87999252023109"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/botorch/optim/optimize.py:652: RuntimeWarning:\nOptimization failed in gen_candidates_scipy with the following warning(s):\n[NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), OptimizationWarning('Optimization failed within scipy.optimize.minimize with status 2 and message ABNORMAL: .'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal')]\nTrying again with a new set of initial conditions."}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/botorch/optim/optimize.py:652: RuntimeWarning:\nOptimization failed on the second try, after generating a new set of initial conditions.\n/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal\n/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 12, HV: 53.60696699268871"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/botorch/optim/optimize.py:652: RuntimeWarning:\nOptimization failed in gen_candidates_scipy with the following warning(s):\n[NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), OptimizationWarning('Optimization failed within scipy.optimize.minimize with status 2 and message ABNORMAL: .'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), OptimizationWarning('Optimization failed within scipy.optimize.minimize with status 2 and message ABNORMAL: .'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), OptimizationWarning('Optimization failed within scipy.optimize.minimize with status 2 and message ABNORMAL: .')]\nTrying again with a new set of initial conditions."}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal\n/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 13, HV: 54.34329480324962"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/botorch/optim/optimize.py:65
12: RuntimeWarning:\nOptimization failed in gen_candidates_scipy with the following warning(s):\n[NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-07 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-06 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-05 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-04 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-03 to the diagonal'), OptimizationWarning('Optimization failed within scipy.optimize.minimize with status 2 and message ABNORMAL: .'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal')]\nTrying again with a new set of initial conditions."}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/botorch/optim/optimize.py:652: RuntimeWarning:\nOptimization failed on the second try, after generating a new set of initial conditions.\n/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal\n/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 14, HV: 54.822694516835085"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 15, HV: 55.290761678067156"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal\n/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 16, HV: 55.72412004820295"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/botorch/optim/optimize.py:652: RuntimeWarning:\nOptimization failed in gen_candidates_scipy with the following warning(s):\n[NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), OptimizationWarning('Optimization failed within scipy.optimize.minimize with status 2 and message ABNORMAL: .'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal')]\nTrying again with a new set of initial conditions."}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/botorch/optim/optimize.py:652: RuntimeWarning:\nOptimization failed on the second try, after generating a new set of initial conditions.\n/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal\n/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 17, HV: 55.9226663252187"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 18, HV: 56.275792468420995"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/botorch/optim/optimize.py:652: RuntimeWarning:\nOptimization failed in gen_candidates_scipy with the following warning(s):\n[NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-07 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-06 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-05 to the diagonal'), OptimizationWarning('Optimization failed within scipy.optimize.minimize with status 2 and message ABNORMAL: .'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-07 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-06 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-05 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-07 to the diagonal'), OptimizationWarning('Optimization failed within scipy.optimize.minimize with status 2 and message ABNORMAL: .'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal')]\nTrying again with a new set of initial conditions."}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal\n/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 19, HV: 56.47590017951882"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 20, HV: 56.65521233151773"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 21, HV: 56.83454729153189"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 22, HV: 56.83454729153189"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 23, HV: 57.01271107560452"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 24, HV: 57.190854885503185"}
1),"\n",(0,g.jsx)(e.h2,{id:"plot-qnehvi-pareto-frontier-based-on-model-posterior",children:"Plot qNEHVI Pareto Frontier based on model posterior"}),"\n",(0,g.jsx)(e.p,{children:"The plotted points are samples from the fitted model's posterior, not observed samples."}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'frontier = compute_posterior_pareto_frontier(\n experiment=ehvi_experiment,\n data=ehvi_experiment.fetch_data(),\n primary_objective=metric_b,\n secondary_objective=metric_a,\n absolute_metrics=["a", "b"],\n num_points=20,\n)\n\nrender(plot_pareto_frontier(frontier, CI_level=0.90))\n'})}),"\n",(0,g.jsx)(o.z,{data:t(94079)}),"\n",(0,g.jsx)(e.h2,{id:"qnparego",children:"qNParEGO"}),"\n",(0,g.jsxs)(e.p,{children:["This is a good alternative algorithm for multi-objective optimization when qNEHVI runs\ntoo slowly. We use ",(0,g.jsx)(e.code,{children:"qLogNParEGO"})," acquisition function with Modular BoTorch Model."]}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:"parego_experiment = build_experiment()\nparego_data = initialize_experiment(parego_experiment)\n"})}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'parego_hv_list = []\nparego_model = None\nfor i in range(N_BATCH):\n parego_model = Models.BOTORCH_MODULAR(\n experiment=parego_experiment,\n data=parego_data,\n botorch_acqf_class=qLogNParEGO,\n )\n generator_run = parego_model.gen(1)\n trial = parego_experiment.new_trial(generator_run=generator_run)\n trial.run()\n parego_data = Data.from_multiple_data([parego_data, trial.fetch_data()])\n\n exp_df = exp_to_df(parego_experiment)\n outcomes = np.array(exp_df[["a", "b"]], dtype=np.double)\n try:\n hv = observed_hypervolume(modelbridge=parego_model)\n except:\n hv = 0\n print("Failed to compute hv")\n parego_hv_list.append(hv)\n print(f"Iteration: {i}, HV: {hv}")\n\nparego_outcomes = np.array(exp_to_df(parego_experiment)[["a", "b"]], dtype=np.double)\n'})}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 0, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 1, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 2, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 3, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 4, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 5, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 6, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 7, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 8, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 9, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 10, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 11, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 12, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 13, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 14, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 15, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 16, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 17, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 18, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 19, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 20, HV: 0.0"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal\n/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\nA not p.d., added jitter of 1.0e-08 to the diagonal"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 21, HV: 2.369795709893773"}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 22, HV: 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diagonal"}),"\n",(0,g.jsx)(a.A,{children:"/opt/hostedtoolcache/Python/3.12.8/x64/lib/python3.12/site-packages/botorch/optim/optimize.py:652: RuntimeWarning:\nOptimization failed in gen_candidates_scipy with the following warning(s):\n[OptimizationWarning('Optimization failed within scipy.optimize.minimize with status 2 and message ABNORMAL: .')]\nTrying again with a new set of initial conditions."}),"\n",(0,g.jsx)(a.A,{children:"Iteration: 24, HV: 21.15155359273342"}),"\n",(0,g.jsx)(e.h2,{id:"plot-qnparego-pareto-frontier-based-on-model-posterior",children:"Plot qNParEGO Pareto Frontier based on model posterior"}),"\n",(0,g.jsx)(e.p,{children:"The plotted points are samples from the fitted model's posterior, not observed samples."}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'frontier = compute_posterior_pareto_frontier(\n experiment=parego_experiment,\n data=parego_experiment.fetch_data(),\n primary_objective=metric_b,\n secondary_objective=metric_a,\n absolute_metrics=["a", "b"],\n num_points=20,\n)\n\nrender(plot_pareto_frontier(frontier, CI_level=0.90))\n'})}),"\n",(0,g.jsx)(o.z,{data:t(34049)}),"\n",(0,g.jsx)(e.h2,{id:"plot-empirical-data",children:"Plot empirical data"}),"\n",(0,g.jsx)(e.h4,{id:"plot-observed-hypervolume-with-color-representing-the-iteration-that-a-point-was-generated-on",children:"Plot observed hypervolume, with color representing the iteration that a point was generated on."}),"\n",(0,g.jsxs)(e.p,{children:["To examine optimization process from another perspective, we plot the collected\nobservations under each algorithm where the color corresponds to the BO iteration at\nwhich the point was collected. The plot on the right for ",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsx)(e.mrow,{children:(0,g.jsx)(e.mi,{children:"q"})}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:"q"})]})})}),(0,g.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,g.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"q"})]})})]}),"NEHVI shows that the\n",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsx)(e.mrow,{children:(0,g.jsx)(e.mi,{children:"q"})}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:"q"})]})})}),(0,g.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,g.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"q"})]})})]}),"NEHVI quickly identifies the Pareto frontier and most of its evaluations are very\nclose to the Pareto frontier. ",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsx)(e.mrow,{children:(0,g.jsx)(e.mi,{children:"q"})}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:"q"})]})})}),(0,g.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,g.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"q"})]})})]}),"NParEGO also identifies has many observations close to\nthe Pareto frontier, but relies on optimizing random scalarizations, which is a less\nprincipled way of optimizing the Pareto front compared to ",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsx)(e.mrow,{children:(0,g.jsx)(e.mi,{children:"q"})}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:"q"})]})})}),(0,g.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,g.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"q"})]})})]}),"NEHVI, which explicitly\nattempts focuses on improving the Pareto front. Sobol generates random points and has\nfew points close to the Pareto front."]}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'import matplotlib\nimport numpy as np\nfrom matplotlib import pyplot as plt\nfrom matplotlib.cm import ScalarMappable\n\n%matplotlib inline\n\n\nfig, axes = plt.subplots(1, 3, figsize=(20, 6))\nalgos = ["Sobol", "qNParEGO", "qNEHVI"]\noutcomes_list = [sobol_outcomes, parego_outcomes, ehvi_outcomes]\ncm = matplotlib.colormaps["viridis"]\nBATCH_SIZE = 1\n\nn_results = N_BATCH * BATCH_SIZE + N_INIT\nbatch_number = torch.cat(\n [\n torch.zeros(N_INIT),\n torch.arange(1, N_BATCH + 1).repeat(BATCH_SIZE, 1).t().reshape(-1),\n ]\n).numpy()\nfor i, train_obj in enumerate(outcomes_list):\n x = i\n sc = axes[x].scatter(\n train_obj[:n_results, 0],\n train_obj[:n_results, 1],\n c=batch_number[:n_results],\n alpha=0.8,\n )\n axes[x].set_title(algos[i])\n axes[x].set_xlabel("Objective 1")\n axes[x].set_xlim(-150, 5)\n axes[x].set_ylim(-15, 0)\naxes[0].set_ylabel("Objective 2")\nnorm = plt.Normalize(batch_number.min(), batch_number.max())\nsm = ScalarMappable(norm=norm, cmap=cm)\nsm.set_array([])\nfig.subplots_adjust(right=0.9)\ncbar_ax = fig.add_axes([0.93, 0.15, 0.01, 0.7])\ncbar = fig.colorbar(sm, cax=cbar_ax)\ncbar.ax.set_title("Iteration")\n'})}),"\n",(0,g.jsx)(a.A,{children:"Text(0.5, 1.0, 'Iteration')"}),"\n",(0,g.jsx)(e.p,{children:(0,g.jsx)(e.img,{src:"data:image/image/png;base64,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9XV1fTs2ZONGzeSmZmZxGQiIiKpoaamhh49epCRkZHsKB2SxiIiIiK7p7HIgaWxiIiIyDdL9fHI97//fbZs2cKsWbP417/+1er5ncsw/vCHP2Tt2rX86U9/4qOPPmLu3Ll4PJ6ma1esWMH555/P97//fS6//HIGDRoEwAMPPMCwYcM45ZRTcLvdvPjii1x55ZU4jsNVV10FwL333ss111xDeno6v/jFLwAoKiraZe6dmQ455BCmT59OSUkJf/jDH5g7dy4fffQR2dnZTdfG43GmTZvG+PHjueuuu3j99df5/e9/T79+/fjBD36w19+zDlUcy8/Px+VyUVJS0ux4SUkJxcXFrb7G5/Ph8/laHM/MzNQgUERE5Cu0rM4301hERETkwNFY5JtpLCIiInJgpep45LDDDmPgwIHMmjWLb33rW83OzZkzh7///e88/vjjXHDBBU3HJ0+ezHHHHcfTTz/d7Pjq1auZMWMG06ZNa9bPO++802x5xauvvprjjjuOu+++u6k4dtppp/HLX/6S/Pz8Fjm+LhqN8rOf/Yzhw4fz7rvvNi25eMQRR3DSSSdxzz33cOuttzZdHwqFOPfcc/nVr34FwBVXXMHBBx/MQw89tE/FsQ61OKbX62XMmDG88cYbTcccx+GNN97gsMMOS2IyERER6Qw0FhEREZFk0lhEREREvu7pp58mKyuLY445hrKysqY2ZswY0tPTeeutt5pd36dPnxaFMaBZYay6upqysjImTpzI559/TnV19V7nWrBgAdu3b+fKK69sthfZiSeeyODBg3n55ZdbvOaKK65o9vWRRx7J559/vtf3hg42cwzguuuu49vf/jZjx45l3Lhx3HvvvdTX13PppZcmO5qIiIh0AhqLiIiISDJpLCIiIiJftWrVKqqrqyksLGz1/Pbt25t93adPn1avmzt3LjfffDPz5s2joaGh2bnq6mqysrL2Ktf69esBmpZt/KrBgwczZ86cZsf8fj8FBQXNjuXk5FBZWblX992pwxXHzj33XEpLS7npppvYtm0bo0aNYsaMGbtd11JEREQkUTQWERERkWTSWERERES+ynEcCgsLefzxx1s9//WC01dniO20Zs0ajj76aAYPHszdd99Njx498Hq9vPLKK9xzzz04jnNAsn+Vy+VKaH8drjgGO9a6vPrqq5MdQ0RERDopjUVEREQkmTQWERER6Xx2tR9av379eP3115kwYUKrha898eKLLxIOh3nhhRfo2bNn0/GvL8m4uxxf16tXLwBWrFjBlClTmp1bsWJF0/kDpUPtOSYiIiIiIiIiIiIiItLZpKWlAVBVVdXs+DnnnEM8HufXv/51i9fEYrEW17dm56wtY0zTserqah5++OFWc+xJn2PHjqWwsJC//OUvhMPhpuOvvvoqn332GSeeeOI39rE/OuTMMRERERERERERERERkc5izJgxAPzwhz9k2rRpuFwuzjvvPCZOnMj3v/99pk+fzuLFizn22GPxeDysWrWKp59+mj/84Q+cddZZu+372GOPxev1cvLJJ/P973+furo6HnzwQQoLC9m6dWuLHA888AC/+c1v6N+/P4WFhS1mhgF4PB5uv/12Lr30UiZOnMj5559PSUkJf/jDH+jduzfXXntt4r45rVBxTEREREREREREREREpB0744wzuOaaa/j3v//NY489hjGG8847D4C/
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
1RRmpFOYkUZBRhq1oTDTX3ubDRVVyY4pIiIiIiIiItJmPtm0jYr6RjL9vlbPZ/h9lNXW89mW7W2crPOJ8+XSivvXUo+KYyIiIkky87NVVNQ3kJ8RxLa+XHvZtizy04PUhMK8smxlEhOKiIiIiIiIiLStSDSOMWaXe4q57B1LLIZjsTZOJh2JimMiIiJJsmjjFiyLZoWxnSzLwmXbfLh+UxKSiYiIiIiIiIgkR8+8bHweN42RaKvnGyJR/B43PfOy2zZYJ7RzWcVEtFSTeolEREQ6CcdxgNafggKwLHCM03aBRERERERERESSrHdBDqN7daU2FCHuNP9cJOY41IeijOvXg67ZmUlK2HnEjZ2wlmpSL5GIiEgnMaJbF4wxOMa0OGeMIRp3GNWtaxKSiYiIiIiIiIgkz9XHHEaP3CxKaxuoqG+kLhShor6RstoGehfk8IMphyY7orRzKo6JiIgkyXFDB5Dp91Fe14D5SoHMGEN5fSNpXg8nDhuYxIQiIiIiIiIiIm2vR24291x4EhcePoqsgB8D5AQDXDRhNHdfcCJdsjOSHbFTMFg4CWhmNysnfd306dM55JBDyMjIoLCwkNNOO40VK1Y0uyYUCnHVVVeRl5dHeno6Z555JiUlJXv13tx7dbWIiIgkTPfsLH469Shuf/1dttfW43bteGYlFncIej1cO3kCAwrzk5xSRERERERERKTtFWam8/3J4/nuxENojEQJeD2UhmtZVrMZGmBoVhfy/SqSdTTvvPMOV111FYcccgixWIyf//znHHvssSxbtoy0tDQArr32Wl5++WWefvppsrKyuPrqqznjjDOYO3fuHt9HxTEREZEkmjywL73zcnh56XIWbNiMA4zu3oUThw1ioApjIiIiIiIiItLJuWybuB3n9qWvM2f7ahriYSws0tw+phQP5vuDJpLm9iU7ZoeUqP3C9qaPGTNmNPv6kUceobCwkIULF3LUUUdRXV3NQw89xBNPPMGUKVMAePjhhxkyZAjvv/8+hx66Z0tuqjgmIiKSZH3ycrh64mHJjiEiIiIiIiIiknIaYxF+tfg5Pq7YRNDto8CXCRjqYmFe2LSY7aFafj36NDy2K9lROxzHWDhmz5dE3F0/ADU1Nc2O+3w+fL7dFzarq6sByM3NBWDhwoVEo1GmTp3adM3gwYPp2bMn8+bN2+PimPYcExERERERERERERGRlPR2yQo+qdxMji+NDI8f27KwLZtMT4AsT5D55Wv5oOzzZMeUPdCjRw+ysrKa2vTp03d7veM4/PjHP2bChAkMHz4cgG3btuH1esnOzm52bVFREdu2bdvjLJo5JiIiIiIiIiIiIiIiKemNrZ8B4LVbljP8Lg/V0Qbe3rqCIwoHtHW0Di+OTTwBc6x29rFx40YyMzObjn/TrLGrrrqKpUuXMmfOnP3O8HUqjomIiIiIiIiIiIiISEoqC9fhtna9ZKILm7JwXRsmkn2VmZnZrDi2O1dffTUvvfQS7777Lt27d286XlxcTCQSoaqqqtnssZKSEoqLi/c4i5ZVFBERERERERERERGRlFTkzyRm4rs8H8dQFNizgovsnZ17jiWi7SljDFdffTXPPvssb775Jn369Gl2fsyYMXg8Ht54442mYytWrGDDhg0cdthhe3wfzRwTEREREREREREREZGUdEyXocwvW0c4HsXn8jQ71xiL4LZsphQPTlK6js3BxknAHKu96eOqq67iiSee4PnnnycjI6NpH7GsrCwCgQBZWVlcdtllXHfddeTm5pKZmck111zDYYcdxqGHHrrH91FxTEREREREREREREREUtJRRQOZueVT5pevxR/3kOb2YYC6WJioE2NS0SDG5vdOdkxJkAceeACASZMmNTv+8MMPc8kllwBwzz33YNs2Z555JuFwmGnTpvHnP/95r+6j4piIiIiIiIiIiIiIiKQkr8vNraNO4aFVc3h96zKqog0AZHoCnNhtDBf1OwyXpR2kDoS4sYjvxZKIu+tnTxljvvEav9/P/fffz/3337/PmVQcExERERERERERERGRlBV0+7hmyNFc3O8wVteWYgEDM4tI9/iTHU3aKRXHREREREREREREREQk5WV5g4zJ6wVANBqnsrKeQMCL3+/5hlfKvnCMhZOAmWOJ6CPRVBwTEREREREREREREZF2oaqqgZdfWcw77y6nviGCx21z6Pj+nHjiKHp0z012vA7FGBvH7P+SlSYBfSSaimMiIiIiIiIiIiIiIpLyKirq+M1vX2D9hnI8Hhc+r5tINM6s15eyYNFafvqTExk4oDjZMaUdSL1ynYiIiIiIiIiIiIiIyNc89fSHrFtfRk52GtlZQQIBL5kZAfLyMqisbODBv7+N45hkx+ww4lgJa6lGxTEREREREREREREREUlp1dUNzHt/NQG/F7e7eWnDti0yM/xs2FjOss82JymhtCcqjomIiIiIiIiIiIiISEor2V5DKBzF7/e0et7rdROPOWzbVt3GyToux4BjrAS0ZL+TlrTnmIiIiIiIiIiIiIiIpDSf141tW8TjDh6PCwDjjmG6V0BaGBOxsT/14fWq7JEojrFxzP7PsUpEH4mmfyUiIiIiIiIiIiIiIpLSevTIo3u3XNauK8Xv9+D0LMMZvRYCUTDgYMgYYbO560fEnH64bZU/ZNf0r0NERESkHdqwYgtzXlzEljXbCaT7OHjyUMZMGY53F8tLiIiIiIiIiLRntm1x6ikHc/+fX6cmfSvBcevB5UCDBycOjnFIz3WzoHYega1eTut2RrIjt3sOFg5WQvpJNak3ly0BwuEwo0aNwrIsFi9enOw4IiIi0skcyLGIMYYX/vYmN593Hy88+CaL3vqU2c8v5L7rH+PXF91P+daqhN5PRERE2h99LiIiIh3VERMGctFFE/AfXIZjx4jVuojFdmxolZUVpDArF4/t5cOKD6iMVCY5bfsXN1bCWqrpkMWxn/70p3Tt2jXZMURERKSTOpBjkQ9nfszT983AcRzyu2ST1yWbgm45ZOaks2rJBu7/6eM4jnNA7i0iIiLtgz4XERGRjuywKT0pGGyRGcggJzuNvNx0unfPJT8vA8uyCLoChOIhltcuS3ZUSWEdrjj26quv8tprr3HXXXclO4qIiIh0QgdyLGKMYebjc4hF42TmpmNZXz555fG5ychJY9Xi9SxfsDbh9xYREZH2QZ+LiIhIRxd2wmAbMtIC5Oamk50dxONxNZ23LBvLsog4kSSm7BgcYyespZoOtedYSUkJl19+Oc899xzBYHCPXhMOhwmHw01f19TUHKh4IiIi0sEd6LFITUUdaz/dRDDd1+p5X8BDXXUDKxZ+ztBx/fYuvIiIiLR7+lxEREQ6g2xPFj7bT9gJ47W9Lc7HnBgAed68to4m7Ujqlev2kTGGSy65hCuuuIKxY8fu8eumT59OVlZWU+vRo8cBTCkiIiIdVVuMRYxjwNBsxthXWZaFBThxLasoIiLS2ehzERER6Sz8rgAH54wh6kSIm1izc8YY6mK15HnzGJwxNEkJOw4HC8ckoKE9x/baDTfcsOODnt205cuXc99991FbW8uNN964V/3feOONVFdXN7WNGzceoHciIiIi7VEqjUUy89Ip7JFHQ3241fPRcBTLtug9tPteZRAREZHUlUpjERERkVRxdOFUugd6UBOtoTZWSzgepiHWQGW0koA7yJndz8Ztd6iF85LCsKOwtb/NpGBxLOX/dVx//fVccsklu72mb9++vPnmm8ybNw+fr/kyQ2PHjuXCCy/k0UcfbfW1Pp+vxWtEREREdkqlsYht20w9/zAevu1ZGutCBNL9TeecuENVWR09BhQz8shBe9SfiIiIpL5UGouIiIikigxPJpf3vYJ3St9iQeV86mL1NMZimGgeXjOIVWWGnoEoAbcn2VElRVnGGJPsEImwYcOGZutib9myhWnTpvHf//6X8ePH0737nj1BXVNTQ1ZWFtXV1WRmZh6ouCIiIu2GfjfumbYai8RjcR781dPMeX4B8biD1+chHneIxeIUdMvluvsuoc8wzRwTEZGOQ2ORPaPPRUREpLN6ZvVi/rx0NnWROI5xY4zBsiz6ZeZyxxEn0DMje7/v0dl+P+58v2e+/m08aS33ddtb0foIz0x9NKW+fyk/c2xP9ezZs9nX6enpAPTr12+PB4CSeMbEcUwM2/Lucn8UERGRjqCtxiIut4vLf3MOoycN5Z1nPmTT6m3403yMP24kk84YR16X7ITdS0RERNoPfS4iIiKd0cLtm7h38fvEHBcF/oymz6CjTpzV1eXc+N4MHp56Nl6XK8lJJdV0mOKYpJaayGo21D5PScMcjIkT9HSle/rxdE8/AdvSVFYREZH94XLZjJ82gvHTRiQ7ioiIiIiIiEjS/Hf1UhpjUYqDGc0mZ3hsF3n+IKurypm7dR2Tu/dLYsr2yzE2jrET0k+q6bDFsd69e9NBVoxsd0ob5/Nx2W+JOjXY+LEsm9rIGpZV/ImyxkWMLPgFLmv/p2KKiIikMo1FREREJJk0FhERkY4u5jh8sG0jQXfrq5Z5XW7ixuGj0i0qju0jx1g4Zv9XhEtEH4nWYYtjkhwxp5FPy+8m6tTiswu/8kMpg7gTYnvjXDbWvkjvzDOTmlNEREQklURicRat20xZXQNZAR9j+3Qn4NVsexERERERkV0xX/xnd7v5WJZFXA+LSCtUHJOEKmmYTSheitfObVGtd9l+ovFaNtW9Qq+M07Gs1JtKKSIiItLW3l2+lr+89QFbq2pwnB0bR+dnBLl4wsGcPHpIizFVVV0jdY1hstMDpAd8SUotIiIiIiKSXB7bxeCcAhZs30ym19/ifMxxABiYnd/W0ToMBwuHBMwcS0AfiabimCRUfXQDALbV+j8ttxWkMVZC1KnF68pqy2giIiIiKef91Rv47YtvEYrGyA768bpdxOIOFXWN/PG197Ati5NGDwFg1aZS/vPmEhas2EAsbvB5XBw1si/nTB5Fl7zMJL8TERERERGRtndGv+EsLt1KTSRMpvfLhwcdYygL1VMUTOfoHlpSUVpScUwSyv5iLzFjTKvrvBocLOym60REREQ6K8cxPDJ7IQ2RKEWZaU1jJ7fLJj8jSFltPf+c+xFThw9g1YZSbnv0NarqQgT9HvxeN+FojJfe+4yPVm3ht5cfT9d8PXgkIiIiIiKdy9E9+vNJ2TYe/2wxZbV12FjYtoXbY5MfSOPW8VNJ92jFjX3Vkfcc07p2klB5/oOxLQ9xE2pxzhhD3DSQ5x+N2w4kIZ2IiIhI6vi8tJw128vJCvhafagoK+intKaORes2c/9zc6muD1GYk0
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The log hypervolume difference is plotted at each step of the optimization\nfor each of the algorithms."}),"\n",(0,g.jsxs)(e.p,{children:["The plot show that ",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsx)(e.mrow,{children:(0,g.jsx)(e.mi,{children:"q"})}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:"q"})]})})}),(0,g.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,g.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"q"})]})})]}),"NEHVI vastly outperforms ",(0,g.jsxs)(e.span,{className:"katex",children:[(0,g.jsx)(e.span,{className:"katex-mathml",children:(0,g.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,g.jsxs)(e.semantics,{children:[(0,g.jsx)(e.mrow,{children:(0,g.jsx)(e.mi,{children:"q"})}),(0,g.jsx)(e.annotation,{encoding:"application/x-tex",children:"q"})]})})}),(0,g.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,g.jsxs)(e.span,{className:"base",children:[(0,g.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,g.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"q"})]})})]}),"NParEGO which outperforms the Sobol\nbaseline."]}),"\n",(0,g.jsx)(e.pre,{children:(0,g.jsx)(e.code,{className:"language-python",children:'iters = np.arange(1, N_BATCH + 1)\nlog_hv_difference_sobol = np.log10(branin_currin.max_hv - np.asarray(sobol_hv_list))[\n : N_BATCH + 1\n]\nlog_hv_difference_parego = np.log10(branin_currin.max_hv - np.asarray(parego_hv_list))[\n : N_BATCH + 1\n]\nlog_hv_difference_ehvi = np.log10(branin_currin.max_hv - np.asarray(ehvi_hv_list))[\n : N_BATCH + 1\n]\n\nfig, ax = plt.subplots(1, 1, figsize=(8, 6))\nax.plot(iters, log_hv_difference_sobol, label="Sobol", linewidth=1.5)\nax.plot(iters, log_hv_difference_parego, label="qNParEGO", linewidth=1.5)\nax.plot(iters, log_hv_difference_ehvi, label="qNEHVI", linewidth=1.5)\nax.set(\n xlabel="number of observations (beyond initial points)",\n ylabel="Log Hypervolume Difference",\n)\nax.legend(loc="lower right")\n'})}),"\n",(0,g.jsx)(a.A,{children:"<matplotlib.legend.Legend at 0x7ff2b78b1df0>"}),"\n",(0,g.jsx)(e.p,{children:(0,g.jsx)(e.img,{src:"data:image/image/png;base64,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