{
"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": [],
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{
"data": {
"text/html": [
""
]
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"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:35] 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\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": {
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"iopub.status.idle": "2022-09-15T17:21:36.175084Z",
"shell.execute_reply": "2022-09-15T17:21:36.174118Z"
},
"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": "2022-09-15T17:21:36.179826Z",
"iopub.status.busy": "2022-09-15T17:21:36.179375Z",
"iopub.status.idle": "2022-09-15T17:21:36.196057Z",
"shell.execute_reply": "2022-09-15T17:21:36.194800Z"
},
"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 09-15 17:21:36] 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 09-15 17:21:36] 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 09-15 17:21:36] 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 09-15 17:21:36] 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 09-15 17:21:36] 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 09-15 17:21:36] 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 09-15 17:21:36] 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 09-15 17:21:36] 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 09-15 17:21:36] 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 09-15 17:21:36] 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",
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"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": "2022-09-15T17:21:36.200439Z",
"iopub.status.busy": "2022-09-15T17:21:36.200065Z",
"iopub.status.idle": "2022-09-15T17:23:29.695701Z",
"shell.execute_reply": "2022-09-15T17:23:29.694747Z"
},
"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 09-15 17:21:36] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.412969, 'x2': 0.328518, 'x3': 0.765503, 'x4': 0.090356, 'x5': 0.084397, 'x6': 0.229964}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.254166, 0.1), 'l2norm': (1.062691, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.400361, 'x2': 0.694227, 'x3': 0.263258, 'x4': 0.456069, 'x5': 0.694066, 'x6': 0.551439}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.216456, 0.1), 'l2norm': (1.377596, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.527782, 'x2': 0.281631, 'x3': 0.459004, 'x4': 0.85833, 'x5': 0.382644, 'x6': 0.843758}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-0.093704, 0.1), 'l2norm': (1.565636, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.964993, 'x2': 0.606123, 'x3': 0.724707, 'x4': 0.674225, 'x5': 0.850825, 'x6': 0.760082}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.032231, 0.1), 'l2norm': (1.856033, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.855739, 'x2': 0.521387, 'x3': 0.202258, 'x4': 0.114507, 'x5': 0.392379, 'x6': 0.866037}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.327491, 0.1), 'l2norm': (1.269839, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.23947, 'x2': 0.446653, 'x3': 0.181172, 'x4': 0.457178, 'x5': 0.601999, 'x6': 0.869284}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.292095, 0.1), 'l2norm': (1.205225, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.852697, 'x2': 0.887604, 'x3': 0.303298, 'x4': 0.77791, 'x5': 0.70816, 'x6': 0.200014}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (0.003432, 0.1), 'l2norm': (1.520647, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.137982, 'x2': 0.164091, 'x3': 0.994962, 'x4': 0.183641, 'x5': 0.758688, 'x6': 0.336802}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.13732, 0.1), 'l2norm': (1.360396, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.998569, 'x2': 0.069484, 'x3': 0.86861, 'x4': 0.020381, 'x5': 0.419802, 'x6': 0.195323}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.086671, 0.1), 'l2norm': (1.346619, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.873837, 'x2': 0.508701, 'x3': 0.475132, 'x4': 0.096994, 'x5': 0.492009, 'x6': 0.077229}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (0.099158, 0.1), 'l2norm': (1.226503, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.425132, 'x2': 0.459248, 'x3': 0.799464, 'x4': 0.641969, 'x5': 0.985835, 'x6': 0.552843}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (0.001006, 0.1), 'l2norm': (1.707721, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.662244, 'x2': 0.670021, 'x3': 0.000235, 'x4': 0.809495, 'x5': 0.215972, 'x6': 0.31156}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:36] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.01377, 0.1), 'l2norm': (1.357761, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:48] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.332177, 'x2': 0.432272, 'x3': 0.145211, 'x4': 0.289302, 'x5': 0.50205, 'x6': 0.86715}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:21:48] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-0.933392, 0.1), 'l2norm': (1.213185, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:22:44] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.337652, 'x2': 0.442638, 'x3': 0.213407, 'x4': 0.258784, 'x5': 0.410148, 'x6': 0.808832}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:22:44] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-1.360083, 0.1), 'l2norm': (1.081447, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:13] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.317832, 'x2': 0.429257, 'x3': 0.210136, 'x4': 0.19964, 'x5': 0.374641, 'x6': 0.772252}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:13] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.580677, 0.1), 'l2norm': (1.173073, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:15] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.319015, 'x2': 0.438675, 'x3': 0.21249, 'x4': 0.18008, 'x5': 0.315566, 'x6': 0.792599}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:15] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.700773, 0.1), 'l2norm': (0.988241, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:23] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.279883, 'x2': 0.416912, 'x3': 0.257569, 'x4': 0.132701, 'x5': 0.30657, 'x6': 0.773901}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:23] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-1.805066, 0.1), 'l2norm': (1.05792, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:25] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.288451, 'x2': 0.351195, 'x3': 0.202783, 'x4': 0.130344, 'x5': 0.24475, 'x6': 0.782968}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:25] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-1.7629, 0.1), 'l2norm': (0.930239, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:27] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.255876, 'x2': 0.490113, 'x3': 0.202269, 'x4': 0.103008, 'x5': 0.237842, 'x6': 0.777957}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:27] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-1.147839, 0.1), 'l2norm': (1.084243, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:29] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.326781, 'x2': 0.369115, 'x3': 0.27679, 'x4': 0.151255, 'x5': 0.304935, 'x6': 0.792773}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:23:29] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-1.681368, 0.1), 'l2norm': (0.941332, 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": {
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"[INFO 09-15 17:23:29] 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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hartmann6: -0.254166 (SEM: 0.1)
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