{
"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": [
{
"data": {
"text/html": [
""
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"metadata": {},
"output_type": "display_data"
},
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"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] 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 03-10 16:20:27] 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 03-10 16:20:27] 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 03-10 16:20:27] 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 03-10 16:20:27] 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 03-10 16:20:27] 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 03-10 16:20:27] 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 03-10 16:20:27] 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 03-10 16:20:27] 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 03-10 16:20:27] ax.service.managed_loop: Started full optimization with 30 steps.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 1...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 2...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 3...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 4...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 5...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 6...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 7...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 8...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 9...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 10...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 11...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 12...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:27] ax.service.managed_loop: Running optimization trial 13...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:34] ax.service.managed_loop: Running optimization trial 14...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:39] ax.service.managed_loop: Running optimization trial 15...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:46] ax.service.managed_loop: Running optimization trial 16...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:52] ax.service.managed_loop: Running optimization trial 17...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:20:58] ax.service.managed_loop: Running optimization trial 18...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:21:04] ax.service.managed_loop: Running optimization trial 19...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:21:09] ax.service.managed_loop: Running optimization trial 20...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:21:16] ax.service.managed_loop: Running optimization trial 21...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:21:21] ax.service.managed_loop: Running optimization trial 22...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:21:28] ax.service.managed_loop: Running optimization trial 23...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:21:33] ax.service.managed_loop: Running optimization trial 24...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:21:38] ax.service.managed_loop: Running optimization trial 25...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:21:45] ax.service.managed_loop: Running optimization trial 26...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:21:51] ax.service.managed_loop: Running optimization trial 27...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:21:56] ax.service.managed_loop: Running optimization trial 28...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:22:00] ax.service.managed_loop: Running optimization trial 29...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 03-10 16:22:05] 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': 0.19156183052597178,\n",
" 'x2': 0.1485798481900465,\n",
" 'x3': 0.4834712132516117,\n",
" 'x4': 0.2729624001743349,\n",
" 'x5': 0.3097645699559457,\n",
" 'x6': 0.6659087464722339}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_parameters"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'hartmann6': -3.318429305778832, 'l2norm': 0.9520638752225008}"
]
},
"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: -0.0778091 (SEM: 0)
x1: 0.63458
x2: 0.176737
x3: 0.777269
x4: 0.613891
x5: 0.660853
x6: 0.704404",
"Arm 10_0
hartmann6: -0.380212 (SEM: 0)
x1: 0.196433
x2: 0.0226757
x3: 0.242024
x4: 0.207609
x5: 0.611927
x6: 0.911383",
"Arm 11_0
hartmann6: -0.583376 (SEM: 0)
x1: 0.0440097
x2: 0.192389
x3: 0.377749
x4: 0.442401
x5: 0.465967
x6: 0.30007",
"Arm 12_0
hartmann6: -1.6106 (SEM: 0)
x1: 0.330772
x2: 0.368949
x3: 0.363253
x4: 0.380512
x5: 0.155903
x6: 0.616362",
"Arm 13_0
hartmann6: -1.85926 (SEM: 0)
x1: 0.287121
x2: 0.324009
x3: 0.356923
x4: 0.365169
x5: 0.166141
x6: 0.596033",
"Arm 14_0
hartmann6: -2.03452 (SEM: 0)
x1: 0.238379
x2: 0.266719
x3: 0.347494
x4: 0.346491
x5: 0.170067
x6: 0.575979",
"Arm 15_0
hartmann6: -2.28353 (SEM: 0)
x1: 0.172717
x2: 0.218906
x3: 0.382558
x4: 0.335899
x5: 0.17538
x6: 0.60967",
"Arm 16_0
hartmann6: -2.35009 (SEM: 0)
x1: 0.109694
x2: 0.233142
x3: 0.427889
x4: 0.307123
x5: 0.178532
x6: 0.632251",
"Arm 17_0
hartmann6: -2.27172 (SEM: 0)
x1: 0.0768223
x2: 0.214709
x3: 0.391534
x4: 0.368487
x5: 0.194651
x6: 0.677802",
"Arm 18_0
hartmann6: -2.73317 (SEM: 0)
x1: 0.151869
x2: 0.169254
x3: 0.434747
x4: 0.275345
x5: 0.203366
x6: 0.674002",
"Arm 19_0
hartmann6: -2.84523 (SEM: 0)
x1: 0.200991
x2: 0.119624
x3: 0.44608
x4: 0.235346
x5: 0.226646
x6: 0.714291",
"Arm 1_0
hartmann6: -0.0192442 (SEM: 0)
x1: 0.0151501
x2: 0.829026
x3: 0.12746
x4: 0.54458
x5: 0.641685
x6: 0.952581",
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hartmann6: -2.46217 (SEM: 0)
x1: 0.171408
x2: 0.131226
x3: 0.38267
x4: 0.190713
x5: 0.212948
x6: 0.740176",
"Arm 21_0
hartmann6: -3.03637 (SEM: 0)
x1: 0.214004
x2: 0.103926
x3: 0.486873
x4: 0.280354
x5: 0.240698
x6: 0.685561",
"Arm 22_0
hartmann6: -2.85333 (SEM: 0)
x1: 0.204275
x2: 0.0437911
x3: 0.561739
x4: 0.289041
x5: 0.237209
x6: 0.676117",
"Arm 23_0
hartmann6: -3.19618 (SEM: 0)
x1: 0.240996
x2: 0.131561
x3: 0.479197
x4: 0.291592
x5: 0.26674
x6: 0.655545",
"Arm 24_0
hartmann6: -3.21967 (SEM: 0)
x1: 0.246362
x2: 0.170455
x3: 0.498586
x4: 0.254516
x5: 0.28253
x6: 0.635244",
"Arm 25_0
hartmann6: -3.19533 (SEM: 0)
x1: 0.230524
x2: 0.117977
x3: 0.458876
x4: 0.247796
x5: 0.283335
x6: 0.617518",
"Arm 26_0
hartmann6: -3.08036 (SEM: 0)
x1: 0.316302
x2: 0.140468
x3: 0.478416
x4: 0.257635
x5: 0.277086
x6: 0.627862",
"Arm 27_0
hartmann6: -3.28653 (SEM: 0)
x1: 0.202306
x2: 0.161937
x3: 0.480446
x4: 0.273759
x5: 0.287021
x6: 0.645348",
"Arm 28_0
hartmann6: -3.31844 (SEM: 0)
x1: 0.191562
x2: 0.14858
x3: 0.483471
x4: 0.272962
x5: 0.309765
x6: 0.665909",
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hartmann6: -0.0576683 (SEM: 0)
x1: 0.0799383
x2: 0.555853
x3: 0.169447
x4: 0.412083
x5: 0.779421
x6: 0.448343",
"Arm 3_0
hartmann6: -0.0472933 (SEM: 0)
x1: 0.657353
x2: 0.943917
x3: 0.756923
x4: 0.0775618
x5: 0.120324
x6: 0.353318",
"Arm 4_0
hartmann6: -0.0398775 (SEM: 0)
x1: 0.812888
x2: 0.0362684
x3: 0.803039
x4: 0.554338
x5: 0.000707027
x6: 0.371636",
"Arm 5_0
hartmann6: -0.000565015 (SEM: 0)
x1: 0.0106335
x2: 0.454275
x3: 0.0317208
x4: 0.955978
x5: 0.78306
x6: 0.761874",
"Arm 6_0
hartmann6: -1.01533 (SEM: 0)
x1: 0.408876
x2: 0.459731
x3: 0.356421
x4: 0.391628
x5: 0.118121
x6: 0.663589",
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hartmann6: -0.00613225 (SEM: 0)
x1: 0.782639
x2: 0.956367
x3: 0.883402
x4: 0.00513333
x5: 0.960213
x6: 0.22616",
"Arm 8_0
hartmann6: -0.0333256 (SEM: 0)
x1: 0.171071
x2: 0.146003
x3: 0.870055
x4: 0.6982
x5: 0.299267
x6: 0.0507671",
"Arm 9_0
hartmann6: -0.0345116 (SEM: 0)
x1: 0.856245
x2: 0.88228
x3: 0.128791
x4: 0.522858
x5: 0.0968765
x6: 0.547021"
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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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