{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"originalKey": "e23719d9-8a24-4208-8439-34e7b8270c79"
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"source": [
"# Visualizations\n",
"\n",
"This tutorial illustrates the core visualization utilities available in Ax."
]
},
{
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{
"data": {
"text/html": [
""
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{
"name": "stderr",
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"text": [
"[INFO 12-29 21:28:38] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n"
]
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"data": {
"text/html": [
" \n",
" "
]
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"source": [
"import numpy as np\n",
"from ax.service.ax_client import AxClient, ObjectiveProperties\n",
"\n",
"from ax.modelbridge.cross_validation import cross_validate\n",
"from ax.plot.contour import interact_contour\n",
"from ax.plot.diagnostic import interact_cross_validation\n",
"from ax.plot.scatter import(\n",
" interact_fitted,\n",
" plot_objective_vs_constraints,\n",
" tile_fitted,\n",
")\n",
"from ax.plot.slice import plot_slice\n",
"from ax.utils.measurement.synthetic_functions import hartmann6\n",
"from ax.utils.notebook.plotting import render, init_notebook_plotting\n",
"\n",
"init_notebook_plotting()"
]
},
{
"cell_type": "markdown",
"metadata": {
"code_folding": [],
"hidden_ranges": [],
"originalKey": "8449378f-890e-4e76-8d73-ce2aa4120a69",
"showInput": true
},
"source": [
"## 1. Create experiment and run optimization\n",
"\n",
"The vizualizations require an experiment object and a model fit on the evaluated data. The routine below is a copy of the Service API tutorial, so the explanation here is omitted. Retrieving the experiment and model objects for each API paradigm is shown in the respective tutorials"
]
},
{
"cell_type": "markdown",
"metadata": {
"originalKey": "f7544e06-6c6a-4841-b659-3be6a198a948"
},
"source": [
"#### 1a. Define search space and evaluation function"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"code_folding": [],
"execution": {
"iopub.execute_input": "2022-12-29T21:28:38.466808Z",
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"shell.execute_reply": "2022-12-29T21:28:38.470765Z"
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"executionStartTime": 1627652824829,
"executionStopTime": 1627652824877,
"hidden_ranges": [],
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"requestMsgId": "7495e7e2-1025-4292-b3aa-e953739cef3e"
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"outputs": [],
"source": [
"noise_sd = 0.1\n",
"param_names = [f\"x{i+1}\" for i in range(6)] # x1, x2, ..., x6\n",
"\n",
"def noisy_hartmann_evaluation_function(parameterization):\n",
" x = np.array([parameterization.get(p_name) for p_name in param_names])\n",
" noise1, noise2 = np.random.normal(0, noise_sd, 2)\n",
"\n",
" return {\n",
" \"hartmann6\": (hartmann6(x) + noise1, noise_sd),\n",
" \"l2norm\": (np.sqrt((x ** 2).sum()) + noise2, noise_sd)\n",
" }\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"originalKey": "17a51543-298e-47d4-bcd9-33459fe1169e"
},
"source": [
"#### 1b. Create Experiment"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"code_folding": [],
"execution": {
"iopub.execute_input": "2022-12-29T21:28:38.474912Z",
"iopub.status.busy": "2022-12-29T21:28:38.474328Z",
"iopub.status.idle": "2022-12-29T21:28:38.486766Z",
"shell.execute_reply": "2022-12-29T21:28:38.485961Z"
},
"executionStartTime": 1627654956712,
"executionStopTime": 1627654956823,
"hidden_ranges": [],
"originalKey": "6fca889c-a4ff-42ef-a669-6eb8803de89c",
"requestMsgId": "905eff52-e649-4bd5-abf0-ff69c1549852"
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"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] 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"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] 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]), RangeParameter(name='x3', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x4', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x5', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x6', parameter_type=FLOAT, range=[0.0, 1.0])], parameter_constraints=[]).\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.modelbridge.dispatch_utils: Using Bayesian optimization since there are more ordered parameters than there are categories for the unordered categorical parameters.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.modelbridge.dispatch_utils: Calculating the number of remaining initialization trials based on num_initialization_trials=None max_initialization_trials=None num_tunable_parameters=6 num_trials=None use_batch_trials=False\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=12\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=12\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+GPEI', steps=[Sobol for 12 trials, GPEI for subsequent trials]). Iterations after 12 will take longer to generate due to model-fitting.\n"
]
}
],
"source": [
"ax_client = AxClient()\n",
"ax_client.create_experiment(\n",
" name=\"test_visualizations\",\n",
" parameters=[\n",
" {\n",
" \"name\": p_name,\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" }\n",
" for p_name in param_names\n",
" ],\n",
" objectives={\"hartmann6\": ObjectiveProperties(minimize=True)},\n",
" outcome_constraints=[\"l2norm <= 1.25\"]\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"code_folding": [],
"hidden_ranges": [],
"originalKey": "ab892f7c-4830-4c1d-b476-ec1078ec3faf",
"showInput": false
},
"source": [
"#### 1c. Run the optimization and fit a GP on all data"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"code_folding": [],
"execution": {
"iopub.execute_input": "2022-12-29T21:28:38.489232Z",
"iopub.status.busy": "2022-12-29T21:28:38.488620Z",
"iopub.status.idle": "2022-12-29T21:30:50.353812Z",
"shell.execute_reply": "2022-12-29T21:30:50.353284Z"
},
"executionStartTime": 1627654642967,
"executionStopTime": 1627654862819,
"hidden_ranges": [],
"originalKey": "7269a5ba-45c8-4acf-ac83-a5ea8a52d6c1",
"requestMsgId": "c7a4dea8-fd6d-4e1a-84de-ad973ede0cd7"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/runner/work/Ax/Ax/ax/core/observation.py:274: FutureWarning:\n",
"\n",
"In a future version of pandas, a length 1 tuple will be returned when iterating over a groupby with a grouper equal to a list of length 1. Don't supply a list with a single grouper to avoid this warning.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.509467, 'x2': 0.028962, 'x3': 0.919525, 'x4': 0.718578, 'x5': 0.205345, 'x6': 0.74537}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.294883, 0.1), 'l2norm': (1.540891, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.030807, 'x2': 0.733315, 'x3': 0.805419, 'x4': 0.732529, 'x5': 0.226611, 'x6': 0.99587}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.335388, 0.1), 'l2norm': (1.784087, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.544919, 'x2': 0.9505, 'x3': 0.93452, 'x4': 0.003054, 'x5': 0.693434, 'x6': 0.049953}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (0.070062, 0.1), 'l2norm': (1.534787, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.458143, 'x2': 0.862874, 'x3': 0.585976, 'x4': 0.042028, 'x5': 0.928453, 'x6': 0.167484}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.204773, 0.1), 'l2norm': (1.505643, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.854988, 'x2': 0.117923, 'x3': 0.417829, 'x4': 0.588809, 'x5': 0.235495, 'x6': 0.00535}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.101418, 0.1), 'l2norm': (1.122423, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.060659, 'x2': 0.36236, 'x3': 0.698587, 'x4': 0.533907, 'x5': 0.162588, 'x6': 0.22702}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.089756, 0.1), 'l2norm': (1.01303, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.681922, 'x2': 0.045512, 'x3': 0.276457, 'x4': 0.682553, 'x5': 0.888026, 'x6': 0.926312}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.014906, 0.1), 'l2norm': (1.499251, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.643002, 'x2': 0.806809, 'x3': 0.602528, 'x4': 0.542176, 'x5': 0.873224, 'x6': 0.263903}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.550204, 0.1), 'l2norm': (1.614762, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.438348, 'x2': 0.01965, 'x3': 0.225021, 'x4': 0.70105, 'x5': 0.820094, 'x6': 0.747691}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (0.022785, 0.1), 'l2norm': (1.46755, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.334092, 'x2': 0.049544, 'x3': 0.31188, 'x4': 0.561487, 'x5': 0.623716, 'x6': 0.951681}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.065793, 0.1), 'l2norm': (1.22676, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.013929, 'x2': 0.867573, 'x3': 0.524857, 'x4': 0.61982, 'x5': 0.352199, 'x6': 0.357934}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-0.226878, 0.1), 'l2norm': (1.236159, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.10638, 'x2': 0.925673, 'x3': 0.347194, 'x4': 0.73536, 'x5': 0.144307, 'x6': 0.885829}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.025526, 0.1), 'l2norm': (1.622494, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:51] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.289555, 'x2': 0.68663, 'x3': 0.616159, 'x4': 0.595965, 'x5': 0.395963, 'x6': 0.235655}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:28:51] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.094233, 0.1), 'l2norm': (1.210456, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:29:13] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.2114, 'x2': 0.659825, 'x3': 0.629484, 'x4': 0.576865, 'x5': 0.256249, 'x6': 0.226572}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:29:13] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-0.771727, 0.1), 'l2norm': (1.092837, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:29:40] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.383577, 'x2': 0.690274, 'x3': 0.614337, 'x4': 0.612205, 'x5': 0.333837, 'x6': 0.169309}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:29:40] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.958704, 0.1), 'l2norm': (1.137047, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:29:54] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.411374, 'x2': 0.657816, 'x3': 0.611819, 'x4': 0.603055, 'x5': 0.245093, 'x6': 0.163786}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:29:54] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.631368, 0.1), 'l2norm': (1.141971, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:30:03] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.401157, 'x2': 0.728809, 'x3': 0.619218, 'x4': 0.636153, 'x5': 0.338858, 'x6': 0.118562}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:30:03] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-2.245452, 0.1), 'l2norm': (1.219328, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:30:16] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.433516, 'x2': 0.73424, 'x3': 0.550635, 'x4': 0.632669, 'x5': 0.363638, 'x6': 0.11215}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:30:16] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-2.313931, 0.1), 'l2norm': (1.463567, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:30:34] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.422282, 'x2': 0.697169, 'x3': 0.68871, 'x4': 0.623526, 'x5': 0.330549, 'x6': 0.108302}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:30:34] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.171868, 0.1), 'l2norm': (1.329198, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:30:50] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.405729, 'x2': 0.686861, 'x3': 0.567166, 'x4': 0.646465, 'x5': 0.268599, 'x6': 0.113926}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:30:50] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.101002, 0.1), 'l2norm': (1.257834, 0.1)}.\n"
]
}
],
"source": [
"for i in range(20):\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=noisy_hartmann_evaluation_function(parameters))"
]
},
{
"cell_type": "markdown",
"metadata": {
"originalKey": "72f4d3e7-fa04-43d0-8451-ded292e705df"
},
"source": [
"## 2. Contour plots\n",
"\n",
"The plot below shows the response surface for `hartmann6` metric as a function of the `x1`, `x2` parameters.\n",
"\n",
"The other parameters are fixed in the middle of their respective ranges, which in this example is 0.5 for all of them."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"code_folding": [],
"execution": {
"iopub.execute_input": "2022-12-29T21:30:50.357615Z",
"iopub.status.busy": "2022-12-29T21:30:50.356455Z",
"iopub.status.idle": "2022-12-29T21:30:50.976990Z",
"shell.execute_reply": "2022-12-29T21:30:50.976433Z"
},
"executionStartTime": 1627654870209,
"executionStopTime": 1627654871972,
"hidden_ranges": [],
"originalKey": "843df85c-965d-4a83-9fe1-696225d81c0f",
"requestMsgId": "4a643541-867c-46b6-868d-64337920c2a3"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:30:50] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Remaining parameters are affixed to the middle of their range.\n"
]
},
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