{
"cells": [
{
"cell_type": "markdown",
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"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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""
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"text": [
"[INFO 09-28 16:20:51] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n"
]
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" \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": {
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"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"
]
},
{
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"execution_count": 2,
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"collapsed": false,
"execution": {
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"executionStopTime": 1627652824877,
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"requestMsgId": "7495e7e2-1025-4292-b3aa-e953739cef3e"
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"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": {
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"shell.execute_reply": "2022-09-28T16:20:51.565356Z"
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"executionStartTime": 1627654956712,
"executionStopTime": 1627654956823,
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"requestMsgId": "905eff52-e649-4bd5-abf0-ff69c1549852"
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"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] 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 09-28 16:20:51] 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 09-28 16:20:51] 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 09-28 16:20:51] 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 09-28 16:20:51] 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 09-28 16:20:51] 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 09-28 16:20:51] 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 09-28 16:20:51] 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 09-28 16:20:51] 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 09-28 16:20:51] 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",
")"
]
},
{
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"showInput": false
},
"source": [
"#### 1c. Run the optimization and fit a GP on all data"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
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"collapsed": false,
"execution": {
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"iopub.status.idle": "2022-09-28T16:23:09.939298Z",
"shell.execute_reply": "2022-09-28T16:23:09.938758Z"
},
"executionStartTime": 1627654642967,
"executionStopTime": 1627654862819,
"hidden_ranges": [],
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"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",
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.454946, 'x2': 0.603001, 'x3': 0.063674, 'x4': 0.424514, 'x5': 0.130818, 'x6': 0.075103}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-1.177602, 0.1), 'l2norm': (0.86887, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.721239, 'x2': 0.428901, 'x3': 0.875858, 'x4': 0.549744, 'x5': 0.212166, 'x6': 0.852913}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.915197, 0.1), 'l2norm': (1.691416, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.623067, 'x2': 0.971697, 'x3': 0.616247, 'x4': 0.757515, 'x5': 0.558287, 'x6': 0.175032}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-0.724632, 0.1), 'l2norm': (1.539999, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.264243, 'x2': 0.168695, 'x3': 0.538047, 'x4': 0.003598, 'x5': 0.344249, 'x6': 0.217604}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.432082, 0.1), 'l2norm': (0.782227, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.187313, 'x2': 0.485827, 'x3': 0.430016, 'x4': 0.711261, 'x5': 0.733871, 'x6': 0.243443}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.257618, 0.1), 'l2norm': (1.313912, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.390678, 'x2': 0.960958, 'x3': 0.120741, 'x4': 0.745606, 'x5': 0.439906, 'x6': 0.780262}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.083186, 0.1), 'l2norm': (1.468524, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.735676, 'x2': 0.449008, 'x3': 0.309312, 'x4': 0.992304, 'x5': 0.667596, 'x6': 0.751031}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.063632, 0.1), 'l2norm': (1.601553, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.17627, 'x2': 0.259648, 'x3': 0.39841, 'x4': 0.104464, 'x5': 0.688635, 'x6': 0.714765}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.670639, 0.1), 'l2norm': (0.975103, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.548878, 'x2': 0.988486, 'x3': 0.942464, 'x4': 0.311807, 'x5': 0.244395, 'x6': 0.531932}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.024953, 0.1), 'l2norm': (1.511371, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.046721, 'x2': 0.284299, 'x3': 0.069976, 'x4': 0.68202, 'x5': 0.442875, 'x6': 0.67003}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.484645, 0.1), 'l2norm': (1.112495, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.799768, 'x2': 0.165811, 'x3': 0.726288, 'x4': 0.835844, 'x5': 0.294569, 'x6': 0.051389}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (0.046002, 0.1), 'l2norm': (1.371904, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.612971, 'x2': 0.680151, 'x3': 0.920277, 'x4': 0.419911, 'x5': 0.030181, 'x6': 0.318475}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:20:51] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.22676, 0.1), 'l2norm': (1.147252, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:21:02] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.453214, 'x2': 0.662361, 'x3': 0.0, 'x4': 0.35427, 'x5': 0.098175, 'x6': 0.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:21:02] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.149865, 0.1), 'l2norm': (0.959162, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:21:15] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.410542, 'x2': 0.53153, 'x3': 0.0, 'x4': 0.346654, 'x5': 0.022487, 'x6': 0.080508}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:21:15] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-0.57885, 0.1), 'l2norm': (0.724437, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:21:37] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.47768, 'x2': 0.687741, 'x3': 0.054868, 'x4': 0.42443, 'x5': 0.179838, 'x6': 0.017929}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:21:37] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.524291, 0.1), 'l2norm': (0.997778, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:21:57] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.498703, 'x2': 0.745856, 'x3': 0.095896, 'x4': 0.429057, 'x5': 0.232983, 'x6': 0.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:21:57] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.896443, 0.1), 'l2norm': (1.052623, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:22:25] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.498377, 'x2': 0.809206, 'x3': 0.136792, 'x4': 0.437591, 'x5': 0.271773, 'x6': 0.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:22:25] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-2.094882, 0.1), 'l2norm': (1.134289, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:22:51] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.564269, 'x2': 0.810752, 'x3': 0.162578, 'x4': 0.385179, 'x5': 0.303267, 'x6': 0.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:22:51] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-1.357871, 0.1), 'l2norm': (1.029446, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:23:07] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.476256, 'x2': 0.848307, 'x3': 0.142714, 'x4': 0.478473, 'x5': 0.303303, 'x6': 0.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:23:07] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.556004, 0.1), 'l2norm': (1.048117, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:23:09] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.447768, 'x2': 0.8895, 'x3': 0.13735, 'x4': 0.519652, 'x5': 0.320775, 'x6': 0.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-28 16:23:09] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.8551, 0.1), 'l2norm': (1.061184, 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."
]
},
{
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{
"name": "stderr",
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"text": [
"[INFO 09-28 16:23:09] 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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