{
"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,
"executionStartTime": 1627652821316,
"executionStopTime": 1627652822868,
"hidden_ranges": [],
"originalKey": "101b0e96-5b3d-48c5-bf3c-677b4ddf90c7",
"requestMsgId": "c0dd9aaf-896d-4ea9-912f-1e58d301d114"
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"outputs": [
{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] 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,
"executionStartTime": 1627652824829,
"executionStopTime": 1627652824877,
"hidden_ranges": [],
"originalKey": "28f6cb76-828f-445d-bdda-ba057c87dcd0",
"requestMsgId": "7495e7e2-1025-4292-b3aa-e953739cef3e"
},
"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,
"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 04-26 20:16:12] 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 04-26 20:16:12] 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 04-26 20:16:12] 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 04-26 20:16:12] 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 04-26 20:16:12] 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 04-26 20:16:12] 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 04-26 20:16:12] 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 04-26 20:16:12] 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 04-26 20:16:12] 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 04-26 20:16:12] 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,
"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 04-26 20:16:12] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.647986, 'x2': 0.940565, 'x3': 0.044812, 'x4': 0.575433, 'x5': 0.637394, 'x6': 0.412333}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.04526, 0.1), 'l2norm': (1.381985, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.567233, 'x2': 0.821178, 'x3': 0.977733, 'x4': 0.199389, 'x5': 0.180126, 'x6': 0.868955}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.238117, 0.1), 'l2norm': (1.656251, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.030914, 'x2': 0.442223, 'x3': 0.032014, 'x4': 0.751952, 'x5': 0.529942, 'x6': 0.162994}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-0.172203, 0.1), 'l2norm': (0.921497, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.893565, 'x2': 0.879475, 'x3': 0.362525, 'x4': 0.865657, 'x5': 0.690319, 'x6': 0.10035}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.173078, 0.1), 'l2norm': (1.674019, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.725341, 'x2': 0.354519, 'x3': 0.346764, 'x4': 0.049017, 'x5': 0.922025, 'x6': 0.225903}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (0.191891, 0.1), 'l2norm': (1.229723, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.635386, 'x2': 0.479884, 'x3': 0.430837, 'x4': 0.817347, 'x5': 0.316434, 'x6': 0.137054}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.409751, 0.1), 'l2norm': (1.198406, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.360357, 'x2': 0.127097, 'x3': 0.981938, 'x4': 0.475173, 'x5': 0.716454, 'x6': 0.980746}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.023049, 0.1), 'l2norm': (1.792053, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.603229, 'x2': 0.63944, 'x3': 0.192713, 'x4': 0.065143, 'x5': 0.470419, 'x6': 0.061607}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.180625, 0.1), 'l2norm': (1.117865, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.809156, 'x2': 0.189099, 'x3': 0.794207, 'x4': 0.773438, 'x5': 0.378103, 'x6': 0.268962}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.074947, 0.1), 'l2norm': (1.325708, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.225076, 'x2': 0.0129, 'x3': 0.802195, 'x4': 0.345076, 'x5': 0.688158, 'x6': 0.461337}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.205796, 0.1), 'l2norm': (1.121066, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.143256, 'x2': 0.67861, 'x3': 0.774216, 'x4': 0.926749, 'x5': 0.741571, 'x6': 0.727287}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-0.00976, 0.1), 'l2norm': (1.844292, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.07977, 'x2': 0.49046, 'x3': 0.474706, 'x4': 0.731792, 'x5': 0.419593, 'x6': 0.904151}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:12] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.255761, 0.1), 'l2norm': (1.39581, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:31] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.514753, 'x2': 0.470081, 'x3': 0.353008, 'x4': 0.774696, 'x5': 0.300075, 'x6': 0.133009}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:31] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-0.24639, 0.1), 'l2norm': (1.073419, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:45] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.648421, 'x2': 0.473822, 'x3': 0.368169, 'x4': 0.71098, 'x5': 0.216919, 'x6': 0.130905}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:16:45] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-0.3002, 0.1), 'l2norm': (1.203156, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:17:04] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.59857, 'x2': 0.454225, 'x3': 0.383377, 'x4': 0.957917, 'x5': 0.250776, 'x6': 0.117958}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:17:04] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-0.160542, 0.1), 'l2norm': (1.236019, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:17:26] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.537644, 'x2': 0.532768, 'x3': 0.461756, 'x4': 0.637048, 'x5': 0.354229, 'x6': 0.096646}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:17:26] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-0.608008, 0.1), 'l2norm': (1.122255, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:17:59] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.485691, 'x2': 0.50462, 'x3': 0.515797, 'x4': 0.592812, 'x5': 0.356857, 'x6': 0.131914}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:17:59] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-0.733421, 0.1), 'l2norm': (1.158977, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:18:24] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.467467, 'x2': 0.573445, 'x3': 0.534, 'x4': 0.534673, 'x5': 0.337681, 'x6': 0.095688}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:18:24] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-1.230438, 0.1), 'l2norm': (1.311675, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:19:21] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.423334, 'x2': 0.588478, 'x3': 0.520482, 'x4': 0.490528, 'x5': 0.320158, 'x6': 0.19463}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:19:21] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-1.21523, 0.1), 'l2norm': (1.161382, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:20:01] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.397725, 'x2': 0.593562, 'x3': 0.536781, 'x4': 0.468968, 'x5': 0.400463, 'x6': 0.126085}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:20:01] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-1.383516, 0.1), 'l2norm': (1.121911, 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": [],
"collapsed": false,
"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 04-26 20:20:01] 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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},
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"Arm 0_0
hartmann6: -0.0452601 (SEM: 0.1)
x1: 0.647986
x2: 0.940565
x3: 0.044812
x4: 0.575433
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x6: 0.412333",
"Arm 10_0
hartmann6: -0.00975973 (SEM: 0.1)
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x4: 0.926749
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