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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Loop API Example on Hartmann6\n",
"\n",
"The loop API is the most lightweight way to do optimization in Ax. The user makes one call to `optimize`, which performs all of the optimization under the hood and returns the optimized parameters.\n",
"\n",
"For more customizability of the optimization procedure, consider the Service or Developer API."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
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""
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"metadata": {},
"output_type": "display_data"
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"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] 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",
"\n",
"from ax.plot.contour import plot_contour\n",
"from ax.plot.trace import optimization_trace_single_method\n",
"from ax.service.managed_loop import optimize\n",
"from ax.metrics.branin import branin\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": {},
"source": [
"## 1. Define evaluation function\n",
"\n",
"First, we define an evaluation function that is able to compute all the metrics needed for this experiment. This function needs to accept a set of parameter values and can also accept a weight. It should produce a dictionary of metric names to tuples of mean and standard error for those metrics."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def hartmann_evaluation_function(parameterization):\n",
" x = np.array([parameterization.get(f\"x{i+1}\") for i in range(6)])\n",
" # In our case, standard error is 0, since we are computing a synthetic function.\n",
" return {\"hartmann6\": (hartmann6(x), 0.0), \"l2norm\": (np.sqrt((x ** 2).sum()), 0.0)}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If there is only one metric in the experiment – the objective – then evaluation function can return a single tuple of mean and SEM, in which case Ax will assume that evaluation corresponds to the objective. It can also return only the mean as a float, in which case Ax will treat SEM as unknown and use a model that can infer it. For more details on evaluation function, refer to the \"Trial Evaluation\" section in the docs."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Run optimization\n",
"The setup for the loop is fully compatible with JSON. The optimization algorithm is selected based on the properties of the problem search space."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] 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 12-16 16:39:14] 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 12-16 16:39:14] 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 12-16 16:39:14] 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 12-16 16:39:14] 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 12-16 16:39:14] 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=[ParameterConstraint(1.0*x1 + 1.0*x2 <= 20.0)]).\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] 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 12-16 16:39:14] 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"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Started full optimization with 30 steps.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 1...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 2...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 3...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 4...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 5...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 6...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 7...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 8...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 9...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 10...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 11...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 12...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:14] ax.service.managed_loop: Running optimization trial 13...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:20] ax.service.managed_loop: Running optimization trial 14...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:26] ax.service.managed_loop: Running optimization trial 15...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:32] ax.service.managed_loop: Running optimization trial 16...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:37] ax.service.managed_loop: Running optimization trial 17...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:43] ax.service.managed_loop: Running optimization trial 18...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:49] ax.service.managed_loop: Running optimization trial 19...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:39:55] ax.service.managed_loop: Running optimization trial 20...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:40:02] ax.service.managed_loop: Running optimization trial 21...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:40:08] ax.service.managed_loop: Running optimization trial 22...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:40:14] ax.service.managed_loop: Running optimization trial 23...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:40:20] ax.service.managed_loop: Running optimization trial 24...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:40:26] ax.service.managed_loop: Running optimization trial 25...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:40:32] ax.service.managed_loop: Running optimization trial 26...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:40:38] ax.service.managed_loop: Running optimization trial 27...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:40:44] ax.service.managed_loop: Running optimization trial 28...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:40:50] ax.service.managed_loop: Running optimization trial 29...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-16 16:40:55] ax.service.managed_loop: Running optimization trial 30...\n"
]
}
],
"source": [
"best_parameters, values, experiment, model = optimize(\n",
" parameters=[\n",
" {\n",
" \"name\": \"x1\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" \"value_type\": \"float\", # Optional, defaults to inference from type of \"bounds\".\n",
" \"log_scale\": False, # Optional, defaults to False.\n",
" },\n",
" {\n",
" \"name\": \"x2\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" },\n",
" {\n",
" \"name\": \"x3\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" },\n",
" {\n",
" \"name\": \"x4\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" },\n",
" {\n",
" \"name\": \"x5\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" },\n",
" {\n",
" \"name\": \"x6\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" },\n",
" ],\n",
" experiment_name=\"test\",\n",
" objective_name=\"hartmann6\",\n",
" evaluation_function=hartmann_evaluation_function,\n",
" minimize=True, # Optional, defaults to False.\n",
" parameter_constraints=[\"x1 + x2 <= 20\"], # Optional.\n",
" outcome_constraints=[\"l2norm <= 1.25\"], # Optional.\n",
" total_trials=30, # Optional.\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And we can introspect optimization results:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'x1': 0.40515050898441496,\n",
" 'x2': 0.8764179218174042,\n",
" 'x3': 0.43999128612860505,\n",
" 'x4': 0.526927536356219,\n",
" 'x5': 0.33013261711814934,\n",
" 'x6': 0.0}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_parameters"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'l2norm': 1.2298333498022433, 'hartmann6': -3.029742536290433}"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"means, covariances = values\n",
"means"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For comparison, minimum of Hartmann6 is:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-3.32237"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hartmann6.fmin"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. Plot results\n",
"Here we arbitrarily select \"x1\" and \"x2\" as the two parameters to plot for both metrics, \"hartmann6\" and \"l2norm\"."
]
},
{
"cell_type": "code",
"execution_count": 7,
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hartmann6: -0.00198612 (SEM: 0)
x1: 0.889652
x2: 0.428703
x3: 0.0620403
x4: 0.477204
x5: 0.860003
x6: 0.721345",
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hartmann6: -0.0167531 (SEM: 0)
x1: 0.10483
x2: 0.210858
x3: 0.868591
x4: 0.831949
x5: 0.233748
x6: 0.0911825",
"Arm 11_0
hartmann6: -0.0218554 (SEM: 0)
x1: 0.987825
x2: 0.589285
x3: 0.458667
x4: 0.608483
x5: 0.609408
x6: 0.65044",
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hartmann6: -0.273918 (SEM: 0)
x1: 0.385464
x2: 0.455468
x3: 0.459117
x4: 0.250578
x5: 0.778737
x6: 0.138175",
"Arm 13_0
hartmann6: -0.462499 (SEM: 0)
x1: 0.401178
x2: 0.514379
x3: 0.556813
x4: 0.284481
x5: 0.814183
x6: 0.0889996",
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hartmann6: -0.767672 (SEM: 0)
x1: 0.335496
x2: 0.585843
x3: 0.690025
x4: 0.327102
x5: 0.704439
x6: 0.00724161",
"Arm 15_0
hartmann6: -0.965303 (SEM: 0)
x1: 0.265306
x2: 0.662688
x3: 0.790957
x4: 0.369588
x5: 0.800351
x6: 3.42291e-18",
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hartmann6: -0.952352 (SEM: 0)
x1: 0.386881
x2: 0.609455
x3: 0.796518
x4: 0.335159
x5: 0.620741
x6: 0",
"Arm 17_0
hartmann6: -0.790919 (SEM: 0)
x1: 0.365473
x2: 0.584339
x3: 0.750171
x4: 0.323595
x5: 0.621966
x6: 0",
"Arm 18_0
hartmann6: -1.04434 (SEM: 0)
x1: 0.378463
x2: 0.651943
x3: 0.693635
x4: 0.317981
x5: 0.582421
x6: 0.00419118",
"Arm 19_0
hartmann6: -1.16621 (SEM: 0)
x1: 0.395947
x2: 0.675556
x3: 0.698173
x4: 0.321622
x5: 0.580696
x6: 0.00601455",
"Arm 1_0
hartmann6: -0.000851153 (SEM: 0)
x1: 0.642945
x2: 0.955892
x3: 0.121558
x4: 0.813211
x5: 0.637652
x6: 0.952821",
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hartmann6: -1.29132 (SEM: 0)
x1: 0.410966
x2: 0.719219
x3: 0.647227
x4: 0.316184
x5: 0.564306
x6: 0.00619903",
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hartmann6: -1.38608 (SEM: 0)
x1: 0.433214
x2: 0.762062
x3: 0.609672
x4: 0.313902
x5: 0.552675
x6: 0.00639606",
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hartmann6: -1.43805 (SEM: 0)
x1: 0.443549
x2: 0.792513
x3: 0.578673
x4: 0.313974
x5: 0.540079
x6: 0.00398552",
"Arm 23_0
hartmann6: -1.79343 (SEM: 0)
x1: 0.424673
x2: 0.843107
x3: 0.51404
x4: 0.34521
x5: 0.486941
x6: 3.32876e-12",
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hartmann6: -2.14874 (SEM: 0)
x1: 0.41128
x2: 0.869695
x3: 0.49797
x4: 0.381492
x5: 0.451377
x6: 0.00979608",
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hartmann6: -2.49969 (SEM: 0)
x1: 0.397336
x2: 0.886032
x3: 0.480676
x4: 0.422592
x5: 0.413807
x6: 0.0212643",
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hartmann6: -2.86378 (SEM: 0)
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x2: 0.903814
x3: 0.436524
x4: 0.488533
x5: 0.353269
x6: 0.022968",
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hartmann6: -2.88611 (SEM: 0)
x1: 0.356998
x2: 0.929707
x3: 0.410984
x4: 0.526385
x5: 0.316892
x6: 0.00940525",
"Arm 28_0
hartmann6: -2.80937 (SEM: 0)
x1: 0.3424
x2: 0.909796
x3: 0.400853
x4: 0.517529
x5: 0.310354
x6: 0.0725171",
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hartmann6: -1.14588 (SEM: 0)
x1: 0.505535
x2: 0.656055
x3: 0.81197
x4: 0.379333
x5: 0.877803
x6: 0.0189884",
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hartmann6: -0.0450205 (SEM: 0)
x1: 0.757186
x2: 0.781214
x3: 0.882771
x4: 0.598411
x5: 0.517964
x6: 0.569161",
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hartmann6: -0.0370313 (SEM: 0)
x1: 0.693038
x2: 0.414121
x3: 0.134982
x4: 0.467462
x5: 0.974968
x6: 0.316927",
"Arm 5_0
hartmann6: -0.00927357 (SEM: 0)
x1: 0.95205
x2: 0.491435
x3: 0.186161
x4: 0.826572
x5: 0.391467
x6: 0.341686",
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x1: 0.372392
x2: 0.231501
x3: 0.17215
x4: 0.167916
x5: 0.726338
x6: 0.402787",
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x1: 0.916148
x2: 0.26941
x3: 0.896762
x4: 0.96937
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x6: 0.627427",
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x1: 0.291749
x2: 0.22287
x3: 0.911979
x4: 0.233576
x5: 0.981372
x6: 0.546906",
"Arm 9_0
hartmann6: -0.0801835 (SEM: 0)
x1: 0.54797
x2: 0.432769
x3: 0.755362
x4: 0.829773
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x6: 0.315621"
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"# `plot_single_method` expects a 2-d array of means, because it expects to average means from multiple \n",
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