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Adaptive\nexperimentation is a natural fit for solving many AutoML tasks, which are often\niterative in nature and can involve many expensive trial evaluations."}),"\n",(0,o.jsx)(t.p,{children:"In this tutorial we will use Ax for hyperparameter optimization (HPO), a common AutoML\ntask in which a model's hyperparameters are adjusted to improve model performance.\nHyperparameters refer to the parameters which are set prior to model training or\nfitting, rather than parameters being learned from data. Traditionally, ML engineers use\na combination of domain knowledge, intuition, and manual experimentation comparing many\nmodels with different hyperparameter configurations to determine good hyperparameters.\nAs the number of hyperparameters grows and as models become more expensive to train and\nevaluate sample efficient aproaches to experimentation like Bayesian optimization become\nincreasingly valuable."}),"\n",(0,o.jsxs)(t.p,{children:["In this tutorial we will train an ",(0,o.jsx)(t.code,{children:"SGDClassifier"})," from the popular\n",(0,o.jsx)(t.a,{href:"https://scikit-learn.org/",children:"scikit-learn"})," library to recognize handwritten digits and\ntune the model's hyperparameters to improve its performance. You can read more about the\n",(0,o.jsx)(t.code,{children:"SGDClassifier"})," model in their example\n",(0,o.jsx)(t.a,{href:"https://scikit-learn.org/stable/auto_examples/classification/plot_digits_classification.html",children:"here"}),",\nwhich this tutorial is largely based on. This tutorial will incorporate many advanced\nfeatures in Ax to demonstrate how they can be applied on complex engineering challenges\nin a real-world setting."]}),"\n",(0,o.jsx)(t.h2,{id:"learning-objectives",children:"Learning Objectives"}),"\n",(0,o.jsxs)(t.ul,{children:["\n",(0,o.jsx)(t.li,{children:"Understand how Ax can be used for HPO tasks"}),"\n",(0,o.jsx)(t.li,{children:"Use complex optimization configurations like multiple objectives and outcome\nconstraints to achieve nuanced real-world goals"}),"\n",(0,o.jsx)(t.li,{children:"Use early stopping to save experimentation resources"}),"\n",(0,o.jsx)(t.li,{children:"Analyze the results of the optimization"}),"\n"]}),"\n",(0,o.jsx)(t.h2,{id:"prerequisites",children:"Prerequisites"}),"\n",(0,o.jsxs)(t.ul,{children:["\n",(0,o.jsxs)(t.li,{children:["Familiarity with ",(0,o.jsx)(t.a,{href:"https://scikit-learn.org/",children:"scikit-learn"})," and basic machine learning\nconcepts"]}),"\n",(0,o.jsxs)(t.li,{children:["Understanding of ",(0,o.jsx)(t.a,{href:"../../intro-to-ae",children:"adaptive experimentation"})," and\n",(0,o.jsx)(t.a,{href:"../../intro-to-bo",children:"Bayesian optimization"})]}),"\n",(0,o.jsx)(t.li,{children:(0,o.jsx)(t.a,{href:"../early_stopping",children:"Ask-tell Optimization of Python Functions with early stopping"})}),"\n"]}),"\n",(0,o.jsx)(t.h2,{id:"step-1-import-necessary-modules",children:"Step 1: Import Necessary Modules"}),"\n",(0,o.jsx)(t.p,{children:"First, ensure you have all the necessary imports:"}),"\n",(0,o.jsx)(t.pre,{children:(0,o.jsx)(t.code,{className:"language-python",children:"import time\n\nimport matplotlib.pyplot as plt\n\nimport sklearn.datasets\nimport sklearn.linear_model\nimport sklearn.model_selection\n\nfrom ax.api.client import Client\nfrom ax.api.configs import ChoiceParameterConfig, RangeParameterConfig\n\nfrom pyre_extensions import assert_is_instance\n"})}),"\n",(0,o.jsxs)(t.h2,{id:"step-11-understanding-the-baseline-performance-of-sgdclassifier",children:["Step 1.1: Understanding the baseline performance of ",(0,o.jsx)(t.code,{children:"SGDClassifier"})]}),"\n",(0,o.jsxs)(t.p,{children:["Before we begin HPO, let's understand the task and the performance of ",(0,o.jsx)(t.code,{children:"SGDClassifier"}),"\nwith its default hyperparameters. The following code is largely adapted from the example\non scikit-learn's webiste\n",(0,o.jsx)(t.a,{href:"https://scikit-learn.org/stable/auto_examples/classification/plot_digits_classification.html",children:"here"}),"."]}),"\n",(0,o.jsx)(t.pre,{children:(0,o.jsx)(t.code,{className:"language-python",children:'# Load the digits dataset and display the first 4 images to demonstrate\ndigits = sklearn.datasets.load_digits()\nclasses = list(set(digits.target))\n\n_, axes = plt.subplots(nrows=1, ncols=4, figsize=(10, 3))\nfor ax, image, label in zip(axes, digits.images, digits.target):\n ax.set_axis_off()\n ax.imshow(image, cmap=plt.cm.gray_r, interpolation="nearest")\n ax.set_title("Training: %i" % label)\n'})}),"\n",(0,o.jsx)(t.p,{children:(0,o.jsx)(t.img,{src:"data:image/png;base64,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ldren:(0,o.jsx)(t.code,{className:"language-python",children:"# Instantiate a SGDClassifier with default hyperparameters\nclf = sklearn.linear_model.SGDClassifier()\n\n# Split the data into a training set and a validation set\ntrain_x, valid_x, train_y, valid_y = sklearn.model_selection.train_test_split(\n digits.data, digits.target, test_size=0.20, random_state=0\n)\n\n# Train the classifier on the training set using 10 batches\n#Also time the training.\nbatch_size = len(train_x) // 10\nstart_time = time.time()\nfor i in range(10):\n start_idx = i * batch_size\n end_idx = (i + 1) * batch_size\n\n # Use partial fit to update the model on the current batch\n clf.partial_fit(\n train_x[start_idx:end_idx], train_y[start_idx:end_idx], classes=classe
1s\n )\n\ntraining_time = time.time() - start_time\n\n# Evaluate the classifier on the validation set\nscore = clf.score(valid_x, valid_y)\nscore, training_time\n"})}),"\n",(0,o.jsx)(s.A,{children:"(0.8638888888888889, 0.03519725799560547)"}),"\n",(0,o.jsx)(t.p,{children:"The model performs well, but let's see if we can improve performance by tuning the\nhyperparameters."}),"\n",(0,o.jsx)(t.h2,{id:"step-2-initialize-the-client",children:"Step 2: Initialize the Client"}),"\n",(0,o.jsxs)(t.p,{children:["As always, the first step in running our adaptive experiment with Ax is to create an\ninstance of the ",(0,o.jsx)(t.code,{children:"Client"})," to manage the state of your experiment."]}),"\n",(0,o.jsx)(t.pre,{children:(0,o.jsx)(t.code,{className:"language-python",children:"client = Client()\n"})}),"\n",(0,o.jsx)(t.h2,{id:"step-3-configure-the-experiment",children:"Step 3: Configure the Experiment"}),"\n",(0,o.jsxs)(t.p,{children:["The ",(0,o.jsx)(t.code,{children:"Client"})," expects a series of ",(0,o.jsx)(t.code,{children:"Config"}),"s which define how the experiment will be run.\nWe'll set this up the same way as we did in our previous tutorial."]}),"\n",(0,o.jsxs)(t.p,{children:["Our current task is to tune the hyperparameters of an scikit-learn's\n",(0,o.jsx)(t.a,{href:"https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.SGDClassifier.html",children:"SGDClassifier"}),".\nThese parameters control aspects of the model's training process and configuring them\ncan have dramatic effects on the model's ability to correctly classify inputs. A full\nlist of this model's hyperparameters and appropriate values are available in the\nlibrary's documentation. In this tutorial we will tune the following hyperparameters:"]}),"\n",(0,o.jsxs)(t.ul,{children:["\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"loss:"})," The loss function to be used"]}),"\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"penalty:"})," The penalty (aka regularization term) to be used"]}),"\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"learning_rate:"})," The learning rate schedule"]}),"\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"alpha:"})," Constant that multiplies the regularization term. The higher the value, the\nstronger the regularization"]}),"\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"eta0"}),": The learning rate for training. In this example we will use a constant\nlearning rate schedule"]}),"\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"batch_size"}),": A training parameter which controls how many examples are shown during\na single epoch. We will use all samples in the dataset for each model training, so a\nsmaller batch size will translate to more epochs and vice versa."]}),"\n"]}),"\n",(0,o.jsxs)(t.p,{children:["You will notice some hyperparameters are continuous ranges, some are discrete ranges,\nand some are categorical choices; Ax is able to handle all of these types of parameters\nvia its ",(0,o.jsx)(t.code,{children:"RangeParameterConfig"})," and ",(0,o.jsx)(t.code,{children:"ChoiceParameterConfig"})," classes."]}),"\n",(0,o.jsx)(t.pre,{children:(0,o.jsx)(t.code,{className:"language-python",children:'# Configure and experiment with the desired parameters\nclient.configure_experiment(\n parameters=[\n ChoiceParameterConfig(\n name="loss",\n parameter_type="str",\n values=[\n "hinge",\n "log_loss",\n "squared_hinge",\n "modified_huber",\n "perceptron",\n ],\n is_ordered=False,\n ),\n ChoiceParameterConfig(\n name="penalty",\n parameter_type="str",\n values=["l1", "l2", "elasticnet"],\n is_ordered=False,\n ),\n ChoiceParameterConfig(\n name="learning_rate",\n parameter_type="str",\n values=["constant", "optimal", "invscaling", "adaptive"],\n is_ordered=False,\n ),\n RangeParameterConfig(\n name="alpha",\n bounds=(1e-8, 100),\n parameter_type="float",\n scaling="log", # Sample this parameter in log transformed space\n ),\n RangeParameterConfig(\n name="eta0",\n bounds=(1e-8, 1),\n parameter_type="float",\n scaling="log",\n ),\n RangeParameterConfig(\n name="batch_size",\n bounds=(5, 500),\n parameter_type="int",\n ),\n ]\n)\n'})}),"\n",(0,o.jsx)(s.A,{children:'/home/runner/work/Ax/Ax/ax/api/utils/instantiation/from_config.py:75: AxParameterWarning: sort_values is not specified for ChoiceParameter "loss". Defaulting to False for parameters of ParameterType STRING. To override this behavior (or avoid this warning), specify sort_values during ChoiceParameter construction.\nreturn ChoiceParameter(\n/home/runner/work/Ax/Ax/ax/api/utils/instantiation/from_config.py:75: AxParameterWarning: sort_values is not specified for ChoiceParameter "penalty". Defaulting to False for parameters of ParameterType STRING. To override this behavior (or avoid this warning), specify sort_values during ChoiceParameter construction.\nreturn ChoiceParameter(\n/home/runner/work/Ax/Ax/ax/api/utils/instantiation/from_config.py:75: AxParameterWarning: sort_values is not specified for ChoiceParameter "learning_rate". Defaulting to False for parameters of ParameterType STRING. To override this behavior (or avoid this warning), specify sort_values during ChoiceParameter construction.\nreturn ChoiceParameter('}),"\n",(0,o.jsx)(t.h2,{id:"step-4-configure-optimization",children:"Step 4: Configure Optimization"}),"\n",(0,o.jsxs)(t.p,{children:["Now, we must set up the optimization objective in ",(0,o.jsx)(t.code,{children:"Client"}),", where ",(0,o.jsx)(t.code,{children:"objective"})," is a\nstring that specifies which metric we would like to optimize and the direction (higher\nor lower) that is considered optimal."]}),"\n",(0,o.jsxs)(t.p,{children:["In our example we want to consider both performance and computational cost implications\nof hyperparameter modifications. ",(0,o.jsx)(t.code,{children:"scikit-learn"})," models use a function called ",(0,o.jsx)(t.code,{children:"score"})," to\nreport the mean accuracy of the model, and in our optimization we should seek to\nmaximize this value. Since model training can be a very expensive process, especially\nfor large models, this can represent a significant cost."]}),"\n",(0,o.jsx)(t.p,{children:"Let's configure Ax to maximize score while minimizing training time. We call this a\nmulti-objective optimization, and rather than returning a single best parameterization\nwe return a Pareto frontier of points which represent optimal tradeoffs between all\nmetrics present. Multi-objective optimization is useful for competing metrics where a\ngain in one metric may represent a regression in the other."}),"\n",(0,o.jsx)(t.p,{children:"In these settings we can also specify outcome constraints, which indicate that if a\nmetric result falls outside of the specified threshold we are not interested in any\nresult, regardless of the wins observed in any other metric. For a concrete example,\nimagine Ax finding a parameterization that trains in no time at all but has an score no\nbetter than if the model were guessing at random."}),"\n",(0,o.jsx)(t.p,{children:"For this toy example let's configure Ax to maximize score and minimize training time,\nbut avoid any hyperparameter configurations that result in a mean accuracy score of less\nthan 75% or a training time greater than 1 second."}),"\n",(0,o.jsx)(t.pre,{children:(0,o.jsx)(t.code,{className:"language-python",children:'client.configure_optimization(\n objective="score, -training_time",\n outcome_constraints=["score >= 0.85", "training_time <= 1"],\n)\n'})}),"\n",(0,o.jsx)(t.h2,{id:"step-5-run-trials-with-early-stopping",children:"Step 5: Run Trials with early stopping"}),"\n",(0,o.jsxs)(t.p,{children:["Before we begin our Bayesian optimization loop, we can attach the data we collected from\ntriaing ",(0,o.jsx)(t.code,{children:"SGDClassifier"})," with default hyperparameters. This will give our experiment a\nhead start by providing a datapoint to our surrogate model. Because these are the\ndefault settings provided by ",(0,o.jsx)(t.code,{children:"scikit-learn"}),", it's likely they will be pretty good and\nwill provide the optimization with a promising start. It is always advantageous to\nattach any existing data to an experiment to improve performance."]}),"\n",(0,o.jsx)(t.pre,{children:(0,o.jsx)(t.code,{className:"language-python",children:'trial_index = client.attach_baseline(\n parameters={\n "loss": clf.loss,\n "penalty": clf.penalty,\n "alpha": clf.alpha,\n "learning_rate": clf.learning_rate,\n "eta0": clf.eta0\n + 1e-8, # Default eta is 0.0, so add a small value to avoid division by zero\n "batch_size": batch_size,\n }\n)\n\nclient.complete_trial(\n trial_index=trial_index,\n raw_data={"score": score, "training_time": training_time},\n)\n'})}),"\n",(0,o.jsx)(s.A,{children:"<enum 'TrialStatus'>.COMPLETED"}),"\n",(0,o.jsxs)(t.p,{children:["After attaching the initial trial, we will begin the experimentation loop by writing a\nfor loop to execute our full experimentation budget of 30 trials. In each iteration we\nwill ask Ax for the next trials (in this case just one), then instantiate an\n",(0,o.jsx)(t.code,{children:"SGDClassifier"})," with the suggested hyperparameters. We will then split the data into\ntrain and test sets. Next we will define an inner loop to perform minibatch training, in\nwhich we divide the train set into a
1number of smaller batches and train one epoch of\nstochastic gradient descent at a time. After each epoch we will report the score and the\ntime."]}),"\n",(0,o.jsxs)(t.p,{children:["Because training machine learning models is expensive, we will utilize Ax's early\nstopping functionality to kill trials unlikely to produce optimal results before they\nhave been completed. After data has been attached we will ask the ",(0,o.jsx)(t.code,{children:"Client"})," whether or\nnot we should stop the trial, and if it advises us to do so we will report it early\nstopped and exit out of the training loop. By early stopping, we proactively save\ncompute without regressing optimization performance."]}),"\n",(0,o.jsx)(t.pre,{children:(0,o.jsx)(t.code,{className:"language-python",children:'for _ in range(20): # Run 20 rounds of 1 trial each\n trials = client.get_next_trials(max_trials=1)\n for trial_index, parameters in trials.items():\n clf = sklearn.linear_model.SGDClassifier(\n loss=parameters["loss"],\n penalty=parameters["penalty"],\n alpha=parameters["alpha"],\n learning_rate=parameters["learning_rate"],\n eta0=parameters["eta0"],\n )\n\n train_x, valid_x, train_y, valid_y = sklearn.model_selection.train_test_split(\n digits.data,\n digits.target,\n test_size=0.20,\n )\n\n batch_size = assert_is_instance(parameters["batch_size"], int)\n num_epochs = len(train_x) // batch_size\n\n start_time = time.time()\n for i in range(0, num_epochs):\n start_idx = i * batch_size\n end_idx = (i + 1) * batch_size\n\n # Use partial fit to update the model on the current batch\n clf.partial_fit(\n train_x[start_idx:end_idx], train_y[start_idx:end_idx], classes=classes\n )\n\n raw_data = {\n "score": clf.score(valid_x, valid_y),\n "training_time": time.time() - start_time,\n }\n\n # On the final epoch call complete_trial and break, else call attach_data\n if i == num_epochs - 1:\n client.complete_trial(\n trial_index=trial_index,\n raw_data=raw_data,\n progression=end_idx, # Use the index of the last example in the batch as the progression value\n )\n break\n\n client.attach_data(\n trial_index=trial_index,\n raw_data=raw_data,\n progression=end_idx,\n )\n\n # If the trial is underperforming, stop it\n if client.should_stop_trial_early(trial_index=trial_index):\n client.mark_trial_early_stopped(trial_index=trial_index)\n break\n\n'})}),"\n",(0,o.jsx)(s.A,{children:"[INFO 05-08 22:43:34] ax.early_stopping.strategies.percentile: Early stoppinging trial 8: Trial objective value 0.8 is worse than 50.0-th percentile (0.8159498207885305) across comparable trials..\n[INFO 05-08 22:44:01] ax.early_stopping.strategies.percentile: Early stoppinging trial 9: Trial objective value 0.8083333333333333 is worse than 50.0-th percentile (0.8112903225806452) across comparable trials..\n[INFO 05-08 22:44:48] ax.early_stopping.strategies.percentile: Early stoppinging trial 11: Trial objective value 0.3527777777777778 is worse than 50.0-th percentile (0.8087606837606838) across comparable trials..\n[INFO 05-08 22:45:12] ax.early_stopping.strategies.percentile: Early stoppinging trial 12: Trial objective value 0.29444444444444445 is worse than 50.0-th percentile (0.7960470085470086) across comparable trials..\n[INFO 05-08 22:45:30] ax.early_stopping.strategies.percentile: Early stoppinging trial 13: Trial objective value 0.14166666666666666 is worse than 50.0-th percentile (0.7833333333333334) across comparable trials..\n[INFO 05-08 22:45:50] ax.early_stopping.strategies.percentile: Early stoppinging trial 14: Trial objective value 0.6916666666666667 is worse than 50.0-th percentile (0.7375) across comparable trials..\n[INFO 05-08 22:46:12] ax.early_stopping.strategies.percentile: Early stoppinging trial 15: Trial objective value 0.4166666666666667 is worse than 50.0-th percentile (0.6916666666666667) across comparable trials..\n[INFO 05-08 22:46:32] ax.early_stopping.strategies.percentile: Early stoppinging trial 16: Trial objective value 0.29444444444444445 is worse than 50.0-th percentile (0.5541666666666667) across comparable trials..\n[INFO 05-08 22:47:20] ax.early_stopping.strategies.percentile: Early stoppinging trial 18: Trial objective value 0.8388888888888889 is worse than 50.0-th percentile (0.8428333025716747) across comparable trials..\n[INFO 05-08 22:48:15] ax.early_stopping.strategies.percentile: Early stoppinging trial 20: Trial objective value 0.4861111111111111 is worse than 50.0-th percentile (0.6916666666666667) across comparable trials.."}),"\n",(0,o.jsx)(t.h2,{id:"step-6-analyze-results",children:"Step 6: Analyze Results"}),"\n",(0,o.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,o.jsx)(t.p,{children:"Since we are optimizing multiple objectives, rather than a single best point we want to\nget the Pareto frontier -- the set of points that presents optimal tradeoffs between\nmaximizing score and minimizing training time."}),"\n",(0,o.jsx)(t.pre,{children:(0,o.jsx)(t.code,{className:"language-python",children:'frontier = client.get_pareto_frontier()\n\n# Frontier is a list of tuples, where each tuple contains the parameters, the metric readings, the trial index, and the arm name for a point on the Pareto frontier\nfor parameters, metrics, trial_index, arm_name in frontier:\n print(f"Trial {trial_index} with {parameters=} and {metrics=}\\n")\n'})}),"\n",(0,o.jsx)(s.A,{children:"Trial 19 with parameters={'alpha': 1e-08, 'eta0': 2.0785865726007548e-08, 'batch_size': 500, 'loss': 'perceptron', 'penalty': 'l2', 'learning_rate': 'invscaling'} and metrics={'score': (np.float64(0.927439676073422), 0.00029892551520375397), 'training_time': (np.float64(0.04615980053989792), 6.503865663735869e-05)}\nTrial 10 with parameters={'alpha': 0.0142668351160523, 'eta0': 1.0, 'batch_size': 500, 'loss': 'hinge', 'penalty': 'l1', 'learning_rate': 'invscaling'} and metrics={'score': (np.float64(0.8871002119084647), 0.00029458280454515656), 'training_time': (np.float64(0.039824911378048514), 6.537514807487683e-05)}\nTrial 0 with parameters={'loss': 'hinge', 'penalty': 'l2', 'alpha': 0.0001, 'learning_rate': 'optimal', 'eta0': 1e-08, 'batch_size': 143} and metrics={'score': (np.float64(0.8653842011548905), 0.0002737580740356988), 'training_time': (np.float64(0.03590925079383221), 6.536118543762476e-05)}"}),"\n",(0,o.jsx)(t.h2,{id:"step-7-compute-analyses",children:"Step 7: Compute Analyses"}),"\n",(0,o.jsxs)(t.p,{children:["Ax can also produce a number of analyses to help interpret the results of the experiment\nvia ",(0,o.jsx)(t.code,{children:"client.compute_analyses"}),". 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,o.jsxs)(t.ul,{children:["\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"Parrellel Coordinates Plot"})," shows which parameterizations were evaluated and what\nmetric values were observed -- this is useful for getting a high level overview of how\nthoroughly the search space was explored and which regions tend to produce which\noutcomes"]}),"\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"Sensitivity Analysis Plot"})," shows which parameters have the largest affect on the\nobjective using\n",(0,o.jsx)(t.a,{href:"https://en.wikipedia.org/wiki/Variance-based_sensitivity_analysis",children:"Sobol Indicies"})]}),"\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"Slice Plot"})," shows how the model predicts a single parameter effects the objective\nalong with a confidence interval"]}),"\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"Contour Plot"})," shows how the model predicts a pair of parameters effects the\nobjective as a 2D surface"]}),"\n",(0,o.jsxs)(t.li,{children:[(0,o.jsx)(t.strong,{children:"Summary"})," lists all trials generated along with their parameterizations,\nobservations, and miscellaneous metadata"]}),"\n",(0,o.jsxs)(t.li,{children:[(0,o.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,o.jsx)(t.pre,{children:(0,o.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,o.jsx)(t.p,{children:(0,o.jsx)(t.strong,{children:"Modeled score vs. training_time"})}),"\n",(0,o.jsx)(t.p,{children:"This plot displays the effects of each arm on the two selected metrics. It is useful for\nunderstanding the trade-off between the two metrics and for visualizing the Pareto\nfrontier."}),"\n",(0,o.jsx)(n.z,{data:r(8891)}),"\n",(0,o.jsx)(t.p,{children:(0,o.jsx)(t.strong,{children:"Summary for Experiment"})}),"\n",(0,o.jsxs)(t.p,{children:["High-level summary of the ",(0,o.jsx)(t.code,{children:"Trial"}),"-s in this 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