{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"originalKey": "e23719d9-8a24-4208-8439-34e7b8270c79"
},
"source": [
"# Visualizations\n",
"\n",
"This tutorial illustrates the core visualization utilities available in Ax."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"code_folding": [],
"collapsed": false,
"execution": {
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{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n"
]
},
{
"data": {
"text/html": [
" \n",
" "
]
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"metadata": {},
"output_type": "display_data"
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],
"source": [
"import numpy as np\n",
"from ax.service.ax_client import AxClient\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": [],
"collapsed": false,
"execution": {
"iopub.execute_input": "2022-08-17T19:19:00.393950Z",
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"iopub.status.idle": "2022-08-17T19:19:00.398966Z",
"shell.execute_reply": "2022-08-17T19:19:00.398206Z"
},
"executionStartTime": 1627652824829,
"executionStopTime": 1627652824877,
"hidden_ranges": [],
"originalKey": "28f6cb76-828f-445d-bdda-ba057c87dcd0",
"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": [],
"collapsed": false,
"execution": {
"iopub.execute_input": "2022-08-17T19:19:00.402279Z",
"iopub.status.busy": "2022-08-17T19:19:00.401713Z",
"iopub.status.idle": "2022-08-17T19:19:00.413168Z",
"shell.execute_reply": "2022-08-17T19:19:00.412567Z"
},
"executionStartTime": 1627654956712,
"executionStopTime": 1627654956823,
"hidden_ranges": [],
"originalKey": "6fca889c-a4ff-42ef-a669-6eb8803de89c",
"requestMsgId": "905eff52-e649-4bd5-abf0-ff69c1549852"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] 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 08-17 19:19:00] 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 08-17 19:19:00] 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 08-17 19:19:00] 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 08-17 19:19:00] 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 08-17 19:19:00] 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 08-17 19:19:00] 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 08-17 19:19:00] 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 08-17 19:19:00] 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 08-17 19:19:00] 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",
" objective_name=\"hartmann6\",\n",
" 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": [],
"collapsed": false,
"execution": {
"iopub.execute_input": "2022-08-17T19:19:00.416788Z",
"iopub.status.busy": "2022-08-17T19:19:00.416233Z",
"iopub.status.idle": "2022-08-17T19:24:22.461102Z",
"shell.execute_reply": "2022-08-17T19:24:22.460399Z"
},
"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": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.522791, 'x2': 0.096022, 'x3': 0.702384, 'x4': 0.399222, 'x5': 0.455364, 'x6': 0.5209}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.829457, 0.1), 'l2norm': (1.183387, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.773745, 'x2': 0.093092, 'x3': 0.247222, 'x4': 0.585888, 'x5': 0.294476, 'x6': 0.473888}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.217803, 0.1), 'l2norm': (0.971702, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.705933, 'x2': 0.801833, 'x3': 0.177404, 'x4': 0.063342, 'x5': 0.193942, 'x6': 0.4848}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (0.006422, 0.1), 'l2norm': (1.268999, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.767577, 'x2': 0.789208, 'x3': 0.518632, 'x4': 0.881343, 'x5': 0.251359, 'x6': 0.098381}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.007809, 0.1), 'l2norm': (1.555475, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.341758, 'x2': 0.789893, 'x3': 0.196094, 'x4': 0.711278, 'x5': 0.840694, 'x6': 0.089609}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-2.108118, 0.1), 'l2norm': (1.363439, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.409433, 'x2': 0.014088, 'x3': 0.359825, 'x4': 0.806296, 'x5': 0.236295, 'x6': 0.84097}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.395754, 0.1), 'l2norm': (1.437141, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.750118, 'x2': 0.531973, 'x3': 0.565425, 'x4': 0.038888, 'x5': 0.886027, 'x6': 0.261148}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.05925, 0.1), 'l2norm': (1.466117, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.03576, 'x2': 0.562891, 'x3': 0.715227, 'x4': 0.90437, 'x5': 0.964702, 'x6': 0.731611}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (0.020015, 0.1), 'l2norm': (1.723995, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.765221, 'x2': 0.352615, 'x3': 0.872664, 'x4': 0.945797, 'x5': 0.147564, 'x6': 0.856606}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.736025, 0.1), 'l2norm': (1.778332, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.341896, 'x2': 0.195082, 'x3': 0.592587, 'x4': 0.365684, 'x5': 0.463302, 'x6': 0.243977}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.457662, 0.1), 'l2norm': (0.986625, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.130236, 'x2': 0.223543, 'x3': 0.612237, 'x4': 0.636673, 'x5': 0.197371, 'x6': 0.522296}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-0.64073, 0.1), 'l2norm': (0.932836, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.201369, 'x2': 0.707901, 'x3': 0.576174, 'x4': 0.944329, 'x5': 0.413604, 'x6': 0.471734}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (0.060777, 0.1), 'l2norm': (1.329567, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:21] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.3098, 'x2': 0.650513, 'x3': 0.18376, 'x4': 0.631801, 'x5': 0.793063, 'x6': 0.143278}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:21] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.371506, 0.1), 'l2norm': (1.181631, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:58] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.308657, 'x2': 0.781304, 'x3': 0.177742, 'x4': 0.613493, 'x5': 0.82053, 'x6': 0.175047}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:19:58] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-1.969521, 0.1), 'l2norm': (1.305342, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:20:28] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.298929, 'x2': 0.800135, 'x3': 0.183083, 'x4': 0.532869, 'x5': 0.827715, 'x6': 0.041594}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:20:28] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-2.347299, 0.1), 'l2norm': (1.477436, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:21:18] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.164342, 'x2': 0.7734, 'x3': 0.153013, 'x4': 0.731503, 'x5': 0.782775, 'x6': 0.119114}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:21:18] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-0.63831, 0.1), 'l2norm': (1.382603, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:21:46] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.34942, 'x2': 0.744105, 'x3': 0.219218, 'x4': 0.506657, 'x5': 0.722175, 'x6': 0.217414}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:21:46] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-1.383296, 0.1), 'l2norm': (1.200137, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:22:45] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.324248, 'x2': 0.768131, 'x3': 0.104987, 'x4': 0.496743, 'x5': 0.895188, 'x6': 0.205844}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:22:45] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-1.58982, 0.1), 'l2norm': (1.431029, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:23:45] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.312934, 'x2': 0.806893, 'x3': 0.134982, 'x4': 0.64607, 'x5': 0.653212, 'x6': 0.091338}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:23:45] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.312109, 0.1), 'l2norm': (1.189659, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:24:22] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.31148, 'x2': 0.783801, 'x3': 0.200755, 'x4': 0.540033, 'x5': 0.528807, 'x6': 0.062417}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-17 19:24:22] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.267889, 0.1), 'l2norm': (1.045947, 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,
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"[INFO 08-17 19:24:22] 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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