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Ax"}),"\n",(0,i.jsxs)(t.li,{children:["Configure and run an experiment using Ax's ",(0,i.jsx)(t.code,{children:"Client"})]}),"\n",(0,i.jsx)(t.li,{children:"Analyze the results of the optimization"}),"\n"]}),"\n",(0,i.jsx)(t.h3,{id:"prerequisites",children:"Prerequisites"}),"\n",(0,i.jsxs)(t.ul,{children:["\n",(0,i.jsx)(t.li,{children:"Familiarity with Python and basic programming concepts"}),"\n",(0,i.jsxs)(t.li,{children:["Understanding of ",(0,i.jsx)(t.a,{href:"/docs/intro-to-ae",children:"adaptive experimentation"})," and\n",(0,i.jsx)(t.a,{href:"/docs/intro-to-bo",children:"Bayesian optimization"})]}),"\n"]}),"\n",(0,i.jsx)(t.h2,{id:"step-1-import-necessary-modules",children:"Step 1: Import Necessary Modules"}),"\n",(0,i.jsx)(t.p,{children:"First, ensure you have all the necessary imports:"}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-python",children:"import numpy as np\nfrom ax.api.client import Client\nfrom ax.api.configs import 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",(0,i.jsxs)(t.span,{className:"katex",children:[(0,i.jsx)(t.span,{className:"katex-mathml",children:(0,i.jsx)(t.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(t.semantics,{children:[(0,i.jsxs)(t.mrow,{children:[(0,i.jsxs)(t.msub,{children:[(0,i.jsx)(t.mi,{children:"x"}),(0,i.jsx)(t.mi,{children:"i"})]}),(0,i.jsx)(t.mo,{children:"\u2208"}),(0,i.jsx)(t.mo,{stretchy:"false",children:"("}),(0,i.jsx)(t.mn,{children:"0"}),(0,i.jsx)(t.mo,{separator:"true",children:","}),(0,i.jsx)(t.mn,{children:"1"}),(0,i.jsx)(t.mo,{stretchy:"false",children:")"})]}),(0,i.jsx)(t.annotation,{encoding:"application/x-tex",children:"x_i \\in (0, 1)"})]})})}),(0,i.jsxs)(t.span,{className:"katex-html","aria-hidden":"true",children:[(0,i.jsxs)(t.span,{className:"base",children:[(0,i.jsx)(t.span,{className:"strut",style:{height:"0.6891em",verticalAlign:"-0.15em"}}),(0,i.jsxs)(t.span,{className:"mord",children:[(0,i.jsx)(t.span,{className:"mord mathnormal",children:"x"}),(0,i.jsx)(t.span,{className:"msupsub",children:(0,i.jsxs)(t.span,{className:"vlist-t vlist-t2",children:[(0,i.jsxs)(t.span,{className:"vlist-r",children:[(0,i.jsx)(t.span,{className:"vlist",style:{height:"0.311

17em"},children:(0,i.jsxs)(t.span,{style:{top:"-2.55em",marginLeft:"0em",marginRight:"0.05em"},children:[(0,i.jsx)(t.span,{className:"pstrut",style:{height:"2.7em"}}),(0,i.jsx)(t.span,{className:"sizing reset-size6 size3 mtight",children:(0,i.jsx)(t.span,{className:"mord mathnormal mtight",children:"i"})})]})}),(0,i.jsx)(t.span,{className:"vlist-s",children:"\u200b"})]}),(0,i.jsx)(t.span,{className:"vlist-r",children:(0,i.jsx)(t.span,{className:"vlist",style:{height:"0.15em"},children:(0,i.jsx)(t.span,{})})})]})})]}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,i.jsx)(t.span,{className:"mrel",children:"\u2208"}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,i.jsxs)(t.span,{className:"base",children:[(0,i.jsx)(t.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,i.jsx)(t.span,{className:"mopen",children:"("}),(0,i.jsx)(t.span,{className:"mord",children:"0"}),(0,i.jsx)(t.span,{className:"mpunct",children:","}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,i.jsx)(t.span,{className:"mord",children:"1"}),(0,i.jsx)(t.span,{className:"mclose",children:")"})]})]})]}),", so we will\ndefine six identical ",(0,i.jsx)(t.code,{children:"RangeParameterConfig"}),"s with these bounds."]}),"\n",(0,i.jsx)(t.p,{children:"You may specify additional features like parameter constraints to further refine the\nsearch space and parameter scaling to help navigate parameters with nonuniform effects."}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-python",children:'# Define six float parameters x1, x2, x3, ... for the Hartmann6 function, which is typically evaluated on the unit hypercube\nparameters = [\n    RangeParameterConfig(\n        name="x1", parameter_type="float", bounds=(0, 1)\n    ),\n    RangeParameterConfig(\n        name="x2", parameter_type="float", bounds=(0, 1)\n    ),\n    RangeParameterConfig(\n        name="x3", parameter_type="float", bounds=(0, 1)\n    ),\n    RangeParameterConfig(\n        name="x4", parameter_type="float", bounds=(0, 1)\n    ),\n    RangeParameterConfig(\n        name="x5", parameter_type="float", bounds=(0, 1)\n    ),\n    RangeParameterConfig(\n        name="x6", parameter_type="float", bounds=(0, 1)\n    ),\n]\n\nclient.configure_experiment(parameters=parameters)\n'})}),"\n",(0,i.jsx)(t.h2,{id:"step-4-configure-optimization",children:"Step 4: Configure Optimization"}),"\n",(0,i.jsxs)(t.p,{children:["Now, we must configure the objective for this optimization, which we do using\n",(0,i.jsx)(t.code,{children:"Client.configure_optimization"}),". This method expects a string ",(0,i.jsx)(t.code,{children:"objective"}),", an expression\ncontaining either a single metric to maximize, a linear combination of metrics to\nmaximize, or a tuple of multiple metrics to jointly maximize. These expressions are\nparsed using ",(0,i.jsx)(t.a,{href:"https://www.sympy.org/en/index.html",children:"SymPy"}),". For example:"]}),"\n",(0,i.jsxs)(t.ul,{children:["\n",(0,i.jsxs)(t.li,{children:[(0,i.jsx)(t.code,{children:'"score"'})," would direct Ax to maximize a metric named score"]}),"\n",(0,i.jsxs)(t.li,{children:[(0,i.jsx)(t.code,{children:'"-loss"'})," would direct Ax to Ax to minimize a metric named loss"]}),"\n",(0,i.jsxs)(t.li,{children:[(0,i.jsx)(t.code,{children:'"task_0 + 0.5 * task_1"'})," would direct Ax to maximize the sum of two task scores,\ndownweighting task_1 by a factor of 0.5"]}),"\n",(0,i.jsxs)(t.li,{children:[(0,i.jsx)(t.code,{children:'"score, -flops"'})," would direct Ax to simultaneously maximize score while minimizing\nflops"]}),"\n"]}),"\n",(0,i.jsxs)(t.p,{children:["See these recipes for more information on configuring\n",(0,i.jsx)(t.a,{href:"../../recipes/multi-objective-optimization",children:"objectives"})," and\n",(0,i.jsx)(t.a,{href:"../../recipes/outcome-constraints",children:"outcome constraints"}),"."]}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-python",children:'metric_name = "hartmann6" # this name is used during the optimization loop in Step 5\nobjective = f"-{metric_name}" # minimization is specified by the negative sign\n\nclient.configure_optimization(objective=objective)\n'})}),"\n",(0,i.jsx)(t.h2,{id:"step-5-run-trials",children:"Step 5: Run Trials"}

1),"\n",(0,i.jsx)(t.p,{children:"Here, we will configure the ask-tell loop."}),"\n",(0,i.jsx)(t.p,{children:"We begin by defining the Hartmann6 function as written above. Remember, this is just an\nexample problem and any Python function can be substituted here."}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-python",children:"# Hartmann6 function\ndef hartmann6(x1, x2, x3, x4, x5, x6):\n    alpha = np.array([1.0, 1.2, 3.0, 3.2])\n    A = np.array([\n        [10, 3, 17, 3.5, 1.7, 8],\n        [0.05, 10, 17, 0.1, 8, 14],\n        [3, 3.5, 1.7, 10, 17, 8],\n        [17, 8, 0.05, 10, 0.1, 14]\n    ])\n    P = 10**-4 * np.array([\n        [1312, 1696, 5569, 124, 8283, 5886],\n        [2329, 4135, 8307, 3736, 1004, 9991],\n        [2348, 1451, 3522, 2883, 3047, 6650],\n        [4047, 8828, 8732, 5743, 1091, 381]\n    ])\n\n    outer = 0.0\n    for i in range(4):\n        inner = 0.0\n        for j, x in enumerate([x1, x2, x3, x4, x5, x6]):\n            inner += A[i, j] * (x - P[i, j])**2\n        outer += alpha[i] * np.exp(-inner)\n    return -outer\n\nhartmann6(0.1, 0.45, 0.8, 0.25, 0.552, 1.0)\n"})}),"\n",(0,i.jsx)(n.A,{children:"np.float64(-0.4878737485613134)"}),"\n",(0,i.jsx)(t.h3,{id:"optimization-loop",children:"Optimization Loop"}),"\n",(0,i.jsxs)(t.p,{children:["We will iteratively call ",(0,i.jsx)(t.code,{children:"client.get_next_trials"}),' to "ask" Ax for a parameterization to\nevaluate, then call ',(0,i.jsx)(t.code,{children:"hartmann6"}),' using those parameters, and finally "tell" Ax the result\nusing ',(0,i.jsx)(t.code,{children:"client.complete_trial"}),"."]}),"\n",(0,i.jsx)(t.p,{children:"This loop will run multiple trials to optimize the function."}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-python",children:'for _ in range(10): # Run 10 rounds of trials\n    # We will request three trials at a time in this example\n    trials = client.get_next_trials(max_trials=3)\n\n    for trial_index, parameters in trials.items():\n        x1 = parameters["x1"]\n        x2 = parameters["x2"]\n        x3 = parameters["x3"]\n        x4 = parameters["x4"]\n        x5 = parameters["x5"]\n        x6 = parameters["x6"]\n\n        result = hartmann6(x1, x2, x3, x4, x5, x6)\n\n        # Set raw_data as a dictionary with metric names as keys and results as values\n        raw_data = {metric_name: result}\n\n        # Complete the trial with the result\n        client.complete_trial(trial_index=trial_index, raw_data=raw_data)\n'})}),"\n",(0,i.jsx)(n.A,{children:"[INFO 06-09 17:02:05] ax.api.client: GenerationStrategy(name='Center+Sobol+MBM:fast', nodes=[CenterGenerationNode(next_node_name='Sobol', use_existing_trials_for_initialization=True), GenerationNode(name='Sobol', generator_specs=[GeneratorSpec(generator_enum=Sobol, generator_key_override=None)], transition_criteria=[MinTrials(transition_to='MBM'), MinTrials(transition_to='MBM')], suggested_experiment_status=ExperimentStatus.INITIALIZATION, pausing_criteria=[MaxTrialsAwaitingData(threshold=5)]), GenerationNode(name='MBM', generator_specs=[GeneratorSpec(generator_enum=BoTorch, generator_key_override=None)], transition_criteria=None, suggested_experiment_status=ExperimentStatus.OPTIMIZATION, pausing_criteria=None)]) chosen based on user input and problem structure.\n[INFO 06-09 17:02:05] ax.api.client: Generated new trial 0 with parameters {'x1': 0.5, 'x2': 0.5, 'x3': 0.5, 'x4': 0.5, 'x5': 0.5, 'x6': 0.5} using GenerationNode CenterOfSearchSpace.\n[INFO 06-09 17:02:05] ax.api.client: Generated new trial 1 with parameters {'x1': 0.54507, 'x2': 0.030051, 'x3': 0.636172, 'x4': 0.183288, 'x5': 0.109244, 'x6': 0.840161} using GenerationNode Sobol.\n[INFO 06-09 17:02:05] ax.api.client: Generated new trial 2 with parameters {'x1': 0.126952, 'x2': 0.935599, 'x3': 0.111927, 'x4': 0.580237, 'x5': 0.727073, 'x6': 0.307275} using GenerationNode Sobol.\n[INFO 06-09 17:02:05] ax.api.client: Trial 0 marked COMPLETED.\n[INFO 06-09 17:02:05] ax.api.client: Trial 1 marked COMPLETED.\n[INFO 06-09 17:02:05] ax.api.client: Trial 2 marked COMPLETED.\n[INFO 06-09 17:02:05] ax.api.client: Generated new trial 3 with parameters {'x1': 0.360873, 'x2': 0.454337, 'x3': 0.872725, 'x4': 0.395083, 'x5': 0.868168, 'x6': 0.09411} using GenerationNode Sobol.\n[INFO 06-09 17:02:05] ax.api.client: Generated new trial 4 with parameters {'x1': 0.967109, 'x2': 0.611289, 'x3': 0.379174, 'x4': 0.872158, 'x5': 0.498388, 'x6': 0.506514} using GenerationNode Sobol.\n[WARNING 06-09 17:02:05] ax.api.client: 3 trials requested but only 2 could be generated.\n[INFO 06-09 17:02:05] ax.api.client: Trial 3 marked COMPLETED.\n[INFO 06-09 17:02:05] ax.api.client: Trial 4 marked COMPLETED.\n[INFO 06-09 17:02:06] ax.api.client: Generated new trial 5 with parameters {'x1': 0.203712, 'x2': 0.539829, 'x3': 0.972701, 'x4': 0.210047, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.\n[WARNING 06-09 17:02:06] ax.api.client: 3 trials requested but only 1 could be generated.\n[INFO 06-09 17:02:06] ax.api.client: Trial 5 marked COMPLETED.\n[INFO 06-09 17:02:07] ax.api.client: Generated new trial 6 with parameters {'x1': 1.0, 'x2': 0.443273, 'x3': 0.0, 'x4': 0.147028, 'x5': 0.401679, 'x6': 1.0} using GenerationNode MBM.\n[INFO 06-09 17:02:07] ax.api.client: Generated new trial 7 with parameters {'x1': 0.0, 'x2': 0.0, 'x3': 0.115507, 'x4': 0.187719, 'x5': 0.0, 'x6': 0.407751} using GenerationNode MBM.\n[INFO 06-09 17:02:07] ax.api.client: Generated new trial 8 with parameters {'x1': 1.0, 'x2': 0.0, 'x3': 1.0, 'x4': 0.22242, 'x5': 0.0, 'x6': 0.712862} using GenerationNode MBM.\n[INFO 06-09 17:02:07] ax.api.client: Trial 6 marked COMPLETED.\n[INFO 06-09 17:02:07] ax.api.client: Trial 7 marked COMPLETED.\n[INFO 06-09 17:02:07] ax.api.client: Trial 8 marked COMPLETED.\n[INFO 06-09 17:02:08] ax.api.client: Generated new trial 9 with parameters {'x1': 0.424625, 'x2': 0.043933, 'x3': 1.0, 'x4': 0.02

11625, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.\n[INFO 06-09 17:02:08] ax.api.client: Generated new trial 10 with parameters {'x1': 0.439597, 'x2': 0.760282, 'x3': 0.815258, 'x4': 0.0, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.\n[INFO 06-09 17:02:08] ax.api.client: Generated new trial 11 with parameters {'x1': 0.410889, 'x2': 0.0, 'x3': 1.0, 'x4': 0.0, 'x5': 0.683521, 'x6': 1.0} using GenerationNode MBM.\n[INFO 06-09 17:02:08] ax.api.client: Trial 9 marked COMPLETED.\n[INFO 06-09 17:02:08] ax.api.client: Trial 10 marked COMPLETED.\n[INFO 06-09 17:02:08] ax.api.client: Trial 11 marked COMPLETED.\n[INFO 06-09 17:02:10] ax.api.client: Generated new trial 12 with parameters {'x1': 0.452384, 'x2': 0.17954, 'x3': 0.604274, 'x4': 0.277632, 'x5': 0.23414, 'x6': 0.701623} using GenerationNode MBM.\n[INFO 06-09 17:02:10] ax.api.client: Generated new trial 13 with parameters {'x1': 0.795537, 'x2': 0.0, 'x3': 0.578587, 'x4': 0.147737, 'x5': 0.014689, 'x6': 1.0} using GenerationNode MBM.\n[INFO 06-09 17:02:10] ax.api.client: Generated new trial 14 with parameters {'x1': 0.241645, 'x2': 0.033682, 'x3': 0.686756, 'x4': 0.196946, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.\n[INFO 06-09 17:02:10] ax.api.client: Trial 12 marked COMPLETED.\n[INFO 06-09 17:02:10] ax.api.client: Trial 13 marked COMPLETED.\n[INFO 06-09 17:02:10] ax.api.client: Trial 14 marked COMPLETED.\n[INFO 06-09 17:02:11] ax.api.client: Generated new trial 15 with parameters {'x1': 0.10989, 'x2': 0.165346, 'x3': 0.481546, 'x4': 0.393877, 'x5': 0.229203, 'x6': 0.962423} using GenerationNode MBM.\n[INFO 06-09 17:02:11] ax.api.client: Generated new trial 16 with parameters {'x1': 0.640097, 'x2': 0.170882, 'x3': 0.396255, 'x4': 0.316366, 'x5': 0.236624, 'x6': 0.0} using GenerationNode MBM.\n[INFO 06-09 17:02:11] ax.api.client: Generated new trial 17 with parameters {'x1': 0.156667, 'x2': 0.169541, 'x3': 1.0, 'x4': 0.198731, 'x5': 0.257877, 'x6': 1.0} using GenerationNode MBM.\n[INFO 06-09 17:02:11] ax.api.client: Trial 15 marked COMPLETED.\n[INFO 06-09 17:02:11] ax.api.client: Trial 16 marked COMPLETED.\n[INFO 06-09 17:02:11] ax.api.client: Trial 17 marked COMPLETED.\n[INFO 06-09 17:02:13] ax.api.client: Generated new trial 18 with parameters {'x1': 0.233365, 'x2': 0.208266, 'x3': 0.368118, 'x4': 0.417064, 'x5': 0.247925, 'x6': 0.675098} using GenerationNode MBM.\n[INFO 06-09 17:02:13] ax.api.client: Generated new trial 19 with parameters {'x1': 0.608267, 'x2': 0.157342, 'x3': 0.387439, 'x4': 0.383513, 'x5': 0.278546, 'x6': 0.676504} using GenerationNode MBM.\n[INFO 06-09 17:02:13] ax.api.client: Generated new trial 20 with parameters {'x1': 0.408685, 'x2': 0.265504, 'x3': 0.580818, 'x4': 0.26215, 'x5': 0.215347, 'x6': 0.689038} using GenerationNode MBM.\n[INFO 06-09 17:02:13] ax.api.client: Trial 18 marked COMPLETED.\n[INFO 06-09 17:02:13] ax.api.client: Trial 19 marked COMPLETED.\n[INFO 06-09 17:02:13] ax.api.client: Trial 20 marked COMPLETED.\n[INFO 06-09 17:02:14] ax.api.client: Generated new trial 21 with parameters {'x1': 0.147548, 'x2': 0.217278, 'x3': 1.0, 'x4': 0.474355, 'x5': 0.0, 'x6': 0.711666} using GenerationNode MBM.\n[INFO 06-09 17:02:14] ax.api.client: Generated new trial 22 with parameters {'x1': 0.1514, 'x2': 0.215632, 'x3': 0.190258, 'x4': 0.0, 'x5': 0.536232, 'x6': 0.713624} using GenerationNode MBM.\n[INFO 06-09 17:02:14] ax.api.client: Generated new trial 23 with parameters {'x1': 0.198349, 'x2': 0.220619, 'x3': 0.869149, 'x4': 0.756628, 'x5': 1.0, 'x6': 0.716454} using GenerationNode MBM.\n[INFO 06-09 17:02:14] ax.api.client: Trial 21 marked COMPLETED.\n[INFO 06-09 17:02:14] ax.api.client: Trial 22 marked COMPLETED.\n[INFO 06-09 17:02:14] ax.api.client: Trial 23 marked COMPLETED.\n[INFO 06-09 17:02:16] ax.api.client: Generated new trial 24 with parameters {'x1': 0.139748, 'x2': 0.0, 'x3': 1.0, 'x4': 0.223724, 'x5': 0.238956, 'x6': 0.630236} using GenerationNode MBM.\n[INFO 06-09 17:02:16] ax.api.client: Generated new trial 25 with parameters {'x1': 0.185059, 'x2': 0.661726, 'x3': 0.82594, 'x4': 0.685625, 'x5': 0.231098, 'x6': 0.67171} using GenerationNode MBM.\n[INFO 06-09 17:02:16] ax.api.client: Generated new trial 26 with parameters {'x1': 0.149077, 'x2': 0.382433, 'x3': 0.0, 'x4': 0.0, 'x5': 0.244154, 'x6': 0.657226} using GenerationNode MBM.\n[INFO 06-09 17:02:16] ax.api.client: Trial 24 marked COMPLETED.\n[INFO 06-09 17:02:16] ax.api.client: Trial 25 marked COMPLETED.\n[INFO 06-09 17:02:16] ax.api.client: Trial 26 marked COMPLETED."}),"\n",(0,i.jsx)(t.h2,{id:"step-6-analyze-results",children:"Step 6: Analyze Results"}),"\n",(0,i.jsx)(t.p,{children:"After running trials, you can analyze the results. Most commonly this means extracting\

1nthe parameterization from the best performing trial you conducted."}),"\n",(0,i.jsxs)(t.p,{children:["Hartmann6 has a known global minimum of ",(0,i.jsxs)(t.span,{className:"katex",children:[(0,i.jsx)(t.span,{className:"katex-mathml",children:(0,i.jsx)(t.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(t.semantics,{children:[(0,i.jsxs)(t.mrow,{children:[(0,i.jsx)(t.mi,{children:"f"}),(0,i.jsx)(t.mo,{stretchy:"false",children:"("}),(0,i.jsx)(t.mi,{children:"x"}),(0,i.jsx)(t.mo,{children:"\u2217"}),(0,i.jsx)(t.mo,{stretchy:"false",children:")"}),(0,i.jsx)(t.mo,{children:"="}),(0,i.jsx)(t.mo,{children:"\u2212"}),(0,i.jsx)(t.mn,{children:"3.322"})]}),(0,i.jsx)(t.annotation,{encoding:"application/x-tex",children:"f(x*) = -3.322"})]})})}),(0,i.jsxs)(t.span,{className:"katex-html","aria-hidden":"true",children:[(0,i.jsxs)(t.span,{className:"base",children:[(0,i.jsx)(t.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,i.jsx)(t.span,{className:"mord mathnormal",style:{marginRight:"0.1076em"},children:"f"}),(0,i.jsx)(t.span,{className:"mopen",children:"("}),(0,i.jsx)(t.span,{className:"mord mathnormal",children:"x"}),(0,i.jsx)(t.span,{className:"mord",children:"\u2217"}),(0,i.jsx)(t.span,{className:"mclose",children:")"}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,i.jsx)(t.span,{className:"mrel",children:"="}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,i.jsxs)(t.span,{className:"base",children:[(0,i.jsx)(t.span,{className:"strut",style:{height:"0.7278em",verticalAlign:"-0.0833em"}}),(0,i.jsx)(t.span,{className:"mord",children:"\u2212"}),(0,i.jsx)(t.span,{className:"mord",children:"3.322"})]})]})]})," at\n",(0,i.jsxs)(t.span,{className:"katex",children:[(0,i.jsx)(t.span,{className:"katex-mathml",children:(0,i.jsx)(t.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(t.semantics,{children:[(0,i.jsxs)(t.mrow,{children:[(0,i.jsx)(t.mi,{children:"x"}),(0,i.jsx)(t.mo,{children:"\u2217"}),(0,i.jsx)(t.mo,{children:"="}),(0,i.jsx)(t.mo,{stretchy:"false",children:"("}),(0,i.jsx)(t.mn,{children:"0.201"}),(0,i.jsx)(t.mo,{separator:"true",children:","}),(0,i.jsx)(t.mn,{children:"0.150"}),(0,i.jsx)(t.mo,{separator:"true",children:","}),(0,i.jsx)(t.mn,{children:"0.477"}),(0,i.jsx)(t.mo,{separator:"true",children:","}),(0,i.jsx)(t.mn,{children:"0.273"}),(0,i.jsx)(t.mo,{separator:"true",children:","}),(0,i.jsx)(t.mn,{children:"0.312"}),(0,i.jsx)(t.mo,{separator:"true",children:","}),(0,i.jsx)(t.mn,{children:"0.657"}),(0,i.jsx)(t.mo,{stretchy:"false",children:")"})]}),(0,i.jsx)(t.annotation,{encoding:"application/x-tex",children:"x* = (0.201, 0.150, 0.477, 0.273, 0.312, 0.657)"})]})})}),(0,i.jsxs)(t.span,{className:"katex-html","aria-hidden":"true",children:[(0,i.jsxs)(t.span,{className:"base",children:[(0,i.jsx)(t.span,{className:"strut",style:{height:"0.4653em"}}),(0,i.jsx)(t.span,{className:"mord mathnormal",children:"x"}),(0,i.jsx)(t.span,{className:"mord",children:"\u2217"}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,i.jsx)(t.span,{className:"mrel",children:"="}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,i.jsxs)(t.span,{className:"base",children:[(0,i.jsx)(t.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,i.jsx)(t.span,{className:"mopen",children:"("}),(0,i.jsx)(t.span,{className:"mord",children:"0.201"}),(0,i.jsx)(t.span,{className:"mpunct",children:","}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,i.jsx)(t.span,{className:"mord",children:"0.150"}),(0,i.jsx)(t.span,{className:"mpunct",children:","}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,i.jsx)(t.span,{className:"mord",children:"0.477"}),(0,i.jsx)(t.span,{className:"mpunct",children:","}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,i.jsx)(t.span,{className:"mord",children:"0.273"}),(0,i.jsx)(t.span,{className:"mpunct",children:","}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,i.jsx)(t.span,{className:"mord",children:"0.312"}),(0,i.jsx)(t.span,{className:"mpunct",children:","}),(0,i.jsx)(t.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,i.jsx)(t.span,{className:"mord",children:"0.657"}),(0,i.jsx)(t.span,{className:"mclose",children:")"})]})]})]}),". Ax is able to identify a point very\nnear to this true optimum ",(0,i.jsx)(t.strong,{children:"using just 30 evaluations."})," This is possible due to the\nsample-efficiency of ",(0,i.jsx)(t.a,{href:"../../intro-to-bo",children:"Bayesian optimization"}),", the optimization method\nwe use under the hood in Ax."]}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-python",children:'best_parameters, prediction, index, name = client.get_best_parameterization()\nprint("Best Parameters:", best_parameters)\nprint("Prediction (mean, variance):", prediction)\n'})}),"\n",(0,i.jsx)(n.A,{children:"Best Parameters: {'x1': 0.2333653056800071, 'x2': 0.20826585358912633, 'x3': 0.36811772534950793, 'x4': 0.4170636776506227, 'x5': 0.24792483640668445, 'x6': 0.6750978891401406}\nPrediction (mean, variance): {'hartmann6': (np.float64(-2.51198544258487), np.float64(0.003399526031064144))}"}),"\n",(0,i.jsx)(t.h2,{id:"step-7-compute-analyses",children:"Step 7: Compute Analyses"}),"\n",(0,i.jsxs)(t.p,{children:["Ax can also produce a number of analyses to help interpret the results of the experiment\nvia ",(0,i.jsx)(t.code,{children:"client.compute_analyses"}

1),". Users can manually select which analyses to run, or can\nallow Ax to select which would be most relevant. In this case Ax selects the following:"]}),"\n",(0,i.jsxs)(t.ul,{children:["\n",(0,i.jsxs)(t.li,{children:[(0,i.jsx)(t.strong,{children:"Arm Effects Plots"})," show the metric value for each\n",(0,i.jsx)(t.a,{href:"https://ax.dev/docs/next/glossary#arm",children:"arm"})," on the experiment. Ax produces one plot\nusing values from its internal surrogate model (this can be helpful for seeing the\ntrue effect of an arm when evaluations are noisy) and another using the raw metric\nvalues as observed."]}),"\n",(0,i.jsxs)(t.li,{children:[(0,i.jsx)(t.strong,{children:"Summary"})," lists all trials generated along with their parameterizations,\nobservations, and miscellaneous metadata"]}),"\n",(0,i.jsxs)(t.li,{children:[(0,i.jsx)(t.strong,{children:"Sensitivity Analysis Plot"})," shows which parameters have the largest affect on the\nobjective using\n",(0,i.jsx)(t.a,{href:"https://en.wikipedia.org/wiki/Variance-based_sensitivity_analysis",children:"Sobol Indicies"})]}),"\n",(0,i.jsxs)(t.li,{children:[(0,i.jsx)(t.strong,{children:"Slice Plot"})," shows how the model predicts a single parameter effects the objective\nalong with a confidence interval"]}),"\n",(0,i.jsxs)(t.li,{children:[(0,i.jsx)(t.strong,{children:"Contour Plot"})," shows how the model predicts a pair of parameters effects the\nobjective as a 2D surface"]}),"\n",(0,i.jsxs)(t.li,{children:[(0,i.jsx)(t.strong,{children:"Cross Validation"})," helps to visualize how well the surrogate model is able to\npredict out of sample points"]}),"\n"]}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-python",children:"# display=True instructs Ax to sort then render the resulting analyses\ncards = client.compute_analyses(display=True)\n"})}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"Modeled Arm Effects on hartmann6"})}),"\n",(0,i.jsx)(t.p,{children:"Modeled effects on hartmann6. This plot visualizes predictions of the true metric\nchanges for each arm based on Ax's model. This is the expected delta you would expect if\nyou (re-)ran that arm. This plot helps in anticipating the outcomes and performance of\narms based on the model's predictions. Note, flat predictions across arms indicate that\nthe model predicts that there is no effect, meaning if you were to re-run the\nexperiment, the delta you would see would be small and fall within the confidence\ninterval indicated in the plot."}),"\n",(0,i.jsx)(s.z,{data:r(22263)}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"Observed Arm Effects on hartmann6"})}),"\n",(0,i.jsx)(t.p,{children:"Observed effects on hartmann6. This plot visualizes the effects from previously-run arms\non a specific metric, providing insights into their performance. This plot allows one to\ncompare and contrast the effectiveness of different arms, highlighting which\nconfigurations have yielded the most favorable outcomes."}),"\n",(0,i.jsx)(s.z,{data:r(70833)}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"Utility Progression"})}),"\n",(0,i.jsx)(t.p,{children:"Shows the best hartmann6 value achieved so far across completed trials (objective is to\nminimize). The x-axis shows trial index. Only completed or early-stopped trials with\ncomplete metric data are included, so there may be gaps if some trials failed, were\nabandoned, or have incomplete data. The y-axis shows cumulative best utility. Only\nimprovements are plotted, so flat segments indicate trials that didn't surpass the\nprevious best. Infeasible trials (violating outcome constraints) don't contribute to the\nimprovements."}),"\n",(0,i.jsx)(s.z,{data:r(41956)}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"Best Trial for Experiment"})}),"\n",(0,i.jsx)(t.p,{children:"Displays the trial with the best objective value based on raw observations. This\nreflects actual measured performance during execution. This trial achieved the optimal\nobjective value and represents the recommended configuration for your optimization goal.\nOnly considering COMPLETED 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Analysis for hartmann6"})}),"\n",(0,i.jsx)(t.p,{children:"Understand how each parameter affects hartmann6 according to a second-order sensitivity\nanalysis."}),"\n",(0,i.jsx)(s.z,{data:r(57481)}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"hartmann6 vs. x5"})}),"\n",(0,i.jsx)(t.p,{children:"The slice plot provides a one-dimensional view of predicted outcomes for hartmann6 as a\nfunction of a single parameter, while keeping all other parameters fixed at their best\ntrial value (Arm 18_0). This visualization helps in understanding the sensitivity and\nimpact of changes in the selected parameter on the predicted metric outcomes."}),"\n",(0,i.jsx)(s.z,{data:r(79269)}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"hartmann6 vs. x6"})}),"\n",(0,i.jsx)(t.p,{children:"The slice plot provides a one-dimensional view of predicted outcomes for hartmann6 as a\nfunction of a single parameter, while keeping all other parameters fixed at their best\ntrial value (Arm 18_0). This visualization helps in understanding the sensitivity and\nimpact of changes in the selected parameter on the predicted metric outcomes."}),"\n",(0,i.jsx)(s.z,{data:r(4266)}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"hartmann6 (Mean) vs. x5, x6"})}),"\n",(0,i.jsx)(t.p,{children:"The contour plot visualizes the predicted outcomes for hartmann6 across a\ntwo-dimensional parameter space, with other parameters held fixed at their best trial\nvalue (Arm 18_0). This plot helps in identifying regions of optimal performance and\nunderstanding how changes in the selected parameters influence the predicted outcomes.\nContour lines represent levels of constant predicted values, providing insights into the\ngradient and potential optima within the parameter space."}),"\n",(0,i.jsx)(s.z,{data:r(52910)}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"Cross Validation for hartmann6 (R\xb2 = 0.93)"})}),"\n",(0,i.jsx)(t.p,{children:"The cross-validation plot displays the model fit for each metric in the experiment. It\nemploys a leave-one-out approach, where the model is trained on all data except one\nsample, which is used for validation. The plot shows the predicted outcome for the\nvalidation set on the y-axis against its actual value on the x-axis. Points that align\nclosely with the dotted diagonal line indicate a strong model fit, signifying accurate\npredictions. Additionally, the plot includes 95% confidence intervals that provide\ninsight into the noise in observations and the uncertainty in model predictions. A\nhorizontal, flat line of predictions indicates that the model has not picked up on\nsufficient signal in the data, and instead is just predicting the mean."}),"\n",(0,i.jsx)(s.z,{data:r(27812)}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"Summary of model fits"})}),"\n",(0,i.jsx)(t.p,{children:"R\xb2 (coefficient of determination) measures how well the model predicts each metric.\nHigher values indicate better model fit. Metrics with R\xb2 >= 0.1 are highlighted in\ngreen."}),"\n",(0,i.jsx)(s.z,{data:r(20388)}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"Generation Strategy Graph"})}),"\n",(0,i.jsxs)(t.p,{children:["GenerationStrategy: Center+Sobol+MBM",":fast"]}),"\n",(0,i.jsx)(t.p,{children:"Visualize the structure of a GenerationStrategy as a directed graph. Each node\nrepresents a GenerationNode in the strategy, and edges represent transitions between\nnodes based on TransitionCriterion. Edge labels show the criterion class names that\ntrigger the transition."}),"\n",(0,i.jsxs)(t.table,{children:[(0,i.jsx)(t.thead,{children:(0,i.jsxs)(t.tr,{children:[(0,i.jsx)(t.th,{style:{textAlign:"right"}}),(0,i.jsx)(t.th,{style:{textAlign:"left"},children:"node_name"}),(0,i.jsx)(t.th,{style:{textAlign:"left"},children:"generators"}),(0,i.jsx)(t.th,{style:{textAlign:"left"},children:"transitions"}),(0,i.jsx)(t.th,{style:{textAlign:"left"},children:"is_current"})]})}),(0,i.jsxs)(t.tbody,{children:[(0,i.jsxs)(t.tr,{children:[(0,i.jsx)(t.td,{style:{textAlign:"right"},children:"0"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"CenterOfSearchSpace"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"nan"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"-> Sobol: AutoTransitionAfterGen"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"False"})]}),(0,i.jsxs)(t.tr,{children:[(0,i.jsx)(t.td,{style:{textAlign:"right"},children:"1"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"Sobol"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"Sobol"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"-> MBM: MinTrials(5), MinTrials(2)"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"False"})]}),(0,i.jsxs)(t.tr,{children:[(0,i.jsx)(t.td,{style:{textAlign:"right"},children:"2"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"MBM"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"BoTorch"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"nan"}),(0,i.jsx)(t.td,{style:{textAlign:"left"},children:"True"})]})]})]}),"\n",(0,i.jsx)(t.p,{children:(0,i.jsx)(t.strong,{children:"Baseline Improvement Healthcheck"})}),"\n",(0,i.jsx)

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