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"cells": [
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"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 09-15 02:32:47] 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 09-15 02:32:47] 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 02:32:47] 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 02:32:47] 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 02:32:47] 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 02:32:47] 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 02:32:47] 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 02:32:47] 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 09-15 02:32:47] ax.service.managed_loop: Started full optimization with 30 steps.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:47] ax.service.managed_loop: Running optimization trial 1...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 2...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 3...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 4...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 5...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 6...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 7...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 8...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 9...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 10...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 11...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 12...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:48] ax.service.managed_loop: Running optimization trial 13...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:54] ax.service.managed_loop: Running optimization trial 14...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:32:59] ax.service.managed_loop: Running optimization trial 15...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:04] ax.service.managed_loop: Running optimization trial 16...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:10] ax.service.managed_loop: Running optimization trial 17...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:15] ax.service.managed_loop: Running optimization trial 18...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:20] ax.service.managed_loop: Running optimization trial 19...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:25] ax.service.managed_loop: Running optimization trial 20...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:30] ax.service.managed_loop: Running optimization trial 21...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:36] ax.service.managed_loop: Running optimization trial 22...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:41] ax.service.managed_loop: Running optimization trial 23...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:46] ax.service.managed_loop: Running optimization trial 24...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:51] ax.service.managed_loop: Running optimization trial 25...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:33:55] ax.service.managed_loop: Running optimization trial 26...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:34:00] ax.service.managed_loop: Running optimization trial 27...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:34:06] ax.service.managed_loop: Running optimization trial 28...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:34:11] ax.service.managed_loop: Running optimization trial 29...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 02:34:15] 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': 0.17175792086072647,\n",
" 'x2': 0.22139587926586693,\n",
" 'x3': 0.48672754738279445,\n",
" 'x4': 0.2939471039831243,\n",
" 'x5': 0.29195961245986535,\n",
" 'x6': 0.6648251581279614}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_parameters"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'hartmann6': -3.223408990687509, 'l2norm': 0.9638840331665048}"
]
},
"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: -0.621769 (SEM: 0)
x1: 0.402881
x2: 0.519896
x3: 0.808794
x4: 0.263642
x5: 0.483005
x6: 0.479485",
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hartmann6: -0.00556795 (SEM: 0)
x1: 0.710347
x2: 0.827351
x3: 0.717838
x4: 0.86011
x5: 0.805492
x6: 0.5756",
"Arm 11_0
hartmann6: -0.145675 (SEM: 0)
x1: 0.17197
x2: 0.753671
x3: 0.547094
x4: 0.882289
x5: 0.0988043
x6: 0.325281",
"Arm 12_0
hartmann6: -0.870246 (SEM: 0)
x1: 0.310816
x2: 0.5599
x3: 0.66414
x4: 0.262765
x5: 0.450429
x6: 0.435467",
"Arm 13_0
hartmann6: -0.754096 (SEM: 0)
x1: 0.288017
x2: 0.598047
x3: 0.549521
x4: 0.22857
x5: 0.468538
x6: 0.393348",
"Arm 14_0
hartmann6: -1.18978 (SEM: 0)
x1: 0.259128
x2: 0.511634
x3: 0.677838
x4: 0.237766
x5: 0.385871
x6: 0.444856",
"Arm 15_0
hartmann6: -1.31751 (SEM: 0)
x1: 0.21997
x2: 0.471755
x3: 0.687636
x4: 0.211149
x5: 0.348144
x6: 0.440441",
"Arm 16_0
hartmann6: -1.54781 (SEM: 0)
x1: 0.180569
x2: 0.457815
x3: 0.697414
x4: 0.169267
x5: 0.324673
x6: 0.507178",
"Arm 17_0
hartmann6: -1.62434 (SEM: 0)
x1: 0.150211
x2: 0.461165
x3: 0.690977
x4: 0.135457
x5: 0.313988
x6: 0.563768",
"Arm 18_0
hartmann6: -2.15402 (SEM: 0)
x1: 0.17356
x2: 0.392335
x3: 0.670103
x4: 0.162717
x5: 0.316122
x6: 0.615742",
"Arm 19_0
hartmann6: -2.56685 (SEM: 0)
x1: 0.191686
x2: 0.34264
x3: 0.636114
x4: 0.187703
x5: 0.319315
x6: 0.671735",
"Arm 1_0
hartmann6: -0.467627 (SEM: 0)
x1: 0.217183
x2: 0.639794
x3: 0.754175
x4: 0.55655
x5: 0.38913
x6: 0.517743",
"Arm 20_0
hartmann6: -2.82445 (SEM: 0)
x1: 0.212492
x2: 0.277217
x3: 0.588966
x4: 0.217566
x5: 0.32787
x6: 0.738716",
"Arm 21_0
hartmann6: -2.52891 (SEM: 0)
x1: 0.21652
x2: 0.226635
x3: 0.640087
x4: 0.20377
x5: 0.259812
x6: 0.78795",
"Arm 22_0
hartmann6: -2.6932 (SEM: 0)
x1: 0.187797
x2: 0.263158
x3: 0.532839
x4: 0.229975
x5: 0.393136
x6: 0.739475",
"Arm 23_0
hartmann6: -2.74372 (SEM: 0)
x1: 0.264919
x2: 0.295277
x3: 0.528557
x4: 0.213041
x5: 0.327328
x6: 0.749514",
"Arm 24_0
hartmann6: -2.87355 (SEM: 0)
x1: 0.206811
x2: 0.285102
x3: 0.572345
x4: 0.28981
x5: 0.326301
x6: 0.747905",
"Arm 25_0
hartmann6: -2.59102 (SEM: 0)
x1: 0.234144
x2: 0.291138
x3: 0.618627
x4: 0.293995
x5: 0.353906
x6: 0.779104",
"Arm 26_0
hartmann6: -3.10765 (SEM: 0)
x1: 0.184217
x2: 0.26031
x3: 0.525743
x4: 0.279585
x5: 0.299749
x6: 0.706335",
"Arm 27_0
hartmann6: -3.22343 (SEM: 0)
x1: 0.171758
x2: 0.221396
x3: 0.486728
x4: 0.293947
x5: 0.29196
x6: 0.664825",
"Arm 28_0
hartmann6: -3.14229 (SEM: 0)
x1: 0.120226
x2: 0.191247
x3: 0.420524
x4: 0.302147
x5: 0.290187
x6: 0.674094",
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hartmann6: -0.0771752 (SEM: 0)
x1: 0.996231
x2: 0.646439
x3: 0.849897
x4: 0.995196
x5: 0.13908
x6: 0.609664",
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hartmann6: -0.514438 (SEM: 0)
x1: 0.178761
x2: 0.685732
x3: 0.242967
x4: 0.375803
x5: 0.617229
x6: 0.183017",
"Arm 4_0
hartmann6: -0.588432 (SEM: 0)
x1: 0.500038
x2: 0.89515
x3: 0.509177
x4: 0.945664
x5: 0.473796
x6: 0.138033",
"Arm 5_0
hartmann6: -0.0279137 (SEM: 0)
x1: 0.396702
x2: 0.278378
x3: 0.848153
x4: 0.090392
x5: 0.825946
x6: 0.0588912",
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hartmann6: -0.350053 (SEM: 0)
x1: 0.167041
x2: 0.67031
x3: 0.203851
x4: 0.285772
x5: 0.0959202
x6: 0.374928",
"Arm 7_0
hartmann6: -0.061582 (SEM: 0)
x1: 0.966608
x2: 0.0530629
x3: 0.397511
x4: 0.105723
x5: 0.0545739
x6: 0.338692",
"Arm 8_0
hartmann6: -0.175442 (SEM: 0)
x1: 0.959177
x2: 0.30908
x3: 0.926258
x4: 0.657565
x5: 0.500267
x6: 0.794314",
"Arm 9_0
hartmann6: -0.0145184 (SEM: 0)
x1: 0.699031
x2: 0.946268
x3: 0.655471
x4: 0.624671
x5: 0.592031
x6: 0.775368"
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"# `plot_single_method` expects a 2-d array of means, because it expects to average means from multiple \n",
"# optimization runs, so we wrap out best objectives array in another array.\n",
"best_objectives = np.array([[trial.objective_mean for trial in experiment.trials.values()]])\n",
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" y=np.minimum.accumulate(best_objectives, axis=1),\n",
" optimum=hartmann6.fmin,\n",
" title=\"Model performance vs. # of iterations\",\n",
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