{
"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 04-25 21:27:06] 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 04-25 21:27:06] 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 04-25 21:27:06] 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 04-25 21:27:06] 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 04-25 21:27:06] 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 04-25 21:27:06] 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 04-25 21:27:06] 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 04-25 21:27:06] 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 04-25 21:27:06] 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 04-25 21:27:06] 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 04-25 21:27:06] 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 04-25 21:27:06] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.156353, 'x2': 0.828955, 'x3': 0.18221, 'x4': 0.993831, 'x5': 0.278476, 'x6': 0.628853}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.00661, 0.1), 'l2norm': (1.519872, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.638525, 'x2': 0.295647, 'x3': 0.056867, 'x4': 0.174938, 'x5': 0.181975, 'x6': 0.433481}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.603912, 0.1), 'l2norm': (0.836981, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.006821, 'x2': 0.841453, 'x3': 0.119364, 'x4': 0.726945, 'x5': 0.762638, 'x6': 0.210246}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-0.058331, 0.1), 'l2norm': (1.35503, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.19718, 'x2': 0.641646, 'x3': 0.99326, 'x4': 0.206919, 'x5': 0.081034, 'x6': 0.066097}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.285483, 0.1), 'l2norm': (1.142436, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.454058, 'x2': 0.160317, 'x3': 0.119512, 'x4': 0.299947, 'x5': 0.989933, 'x6': 0.076605}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.033935, 0.1), 'l2norm': (1.10637, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.604522, 'x2': 0.925746, 'x3': 0.607682, 'x4': 0.265181, 'x5': 0.568391, 'x6': 0.474896}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.019129, 0.1), 'l2norm': (1.650064, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.635463, 'x2': 0.26446, 'x3': 0.618036, 'x4': 0.907142, 'x5': 0.883884, 'x6': 0.555087}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (0.070479, 0.1), 'l2norm': (1.651056, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.80227, 'x2': 0.59793, 'x3': 0.773525, 'x4': 0.867527, 'x5': 0.914255, 'x6': 0.357337}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.019961, 0.1), 'l2norm': (2.048878, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.885401, 'x2': 0.979298, 'x3': 0.52418, 'x4': 0.628868, 'x5': 0.398996, 'x6': 0.143867}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (0.115659, 0.1), 'l2norm': (1.613013, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.652378, 'x2': 0.878267, 'x3': 0.698092, 'x4': 0.167317, 'x5': 0.394397, 'x6': 0.190446}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.039665, 0.1), 'l2norm': (1.253833, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:06] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.925983, 'x2': 0.915254, 'x3': 0.332073, 'x4': 0.883105, 'x5': 0.483516, 'x6': 0.340959}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:07] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-0.004602, 0.1), 'l2norm': (1.678071, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:07] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.171178, 'x2': 0.467583, 'x3': 0.13919, 'x4': 0.224523, 'x5': 0.955353, 'x6': 0.641796}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:07] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.046218, 0.1), 'l2norm': (1.344774, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:20] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.628777, 'x2': 0.232364, 'x3': 0.032492, 'x4': 0.115041, 'x5': 0.081049, 'x6': 0.431374}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:20] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-0.097935, 0.1), 'l2norm': (0.831384, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:29] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.639537, 'x2': 0.316663, 'x3': 0.068793, 'x4': 0.194442, 'x5': 0.226739, 'x6': 0.433794}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:29] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-0.759589, 0.1), 'l2norm': (0.775916, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:37] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.665487, 'x2': 0.293105, 'x3': 0.000115, 'x4': 0.202545, 'x5': 0.258844, 'x6': 0.455193}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:37] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.023126, 0.1), 'l2norm': (1.026266, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:51] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.678476, 'x2': 0.283359, 'x3': 0.0, 'x4': 0.211517, 'x5': 0.302936, 'x6': 0.4686}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:51] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.100207, 0.1), 'l2norm': (0.827118, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:55] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.749384, 'x2': 0.324648, 'x3': 0.0, 'x4': 0.277968, 'x5': 0.307693, 'x6': 0.489239}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:27:55] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-0.520247, 0.1), 'l2norm': (1.035583, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:28:02] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.650144, 'x2': 0.273984, 'x3': 0.0, 'x4': 0.198529, 'x5': 0.326291, 'x6': 0.463495}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:28:02] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-0.90135, 0.1), 'l2norm': (0.997695, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:28:28] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.674411, 'x2': 0.343923, 'x3': 0.0, 'x4': 0.147457, 'x5': 0.299825, 'x6': 0.420233}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:28:28] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-0.556067, 0.1), 'l2norm': (0.951424, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:28:31] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.633521, 'x2': 0.273156, 'x3': 0.0, 'x4': 0.240819, 'x5': 0.28017, 'x6': 0.441031}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:28:31] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-0.882174, 0.1), 'l2norm': (0.865362, 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 04-25 21:28:31] 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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