{
"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": {
"execution": {
"iopub.execute_input": "2022-09-15T17:05:47.492017Z",
"iopub.status.busy": "2022-09-15T17:05:47.491045Z",
"iopub.status.idle": "2022-09-15T17:05:50.650658Z",
"shell.execute_reply": "2022-09-15T17:05:50.649749Z"
}
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n"
]
},
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"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,
"execution": {
"iopub.execute_input": "2022-09-15T17:05:50.717869Z",
"iopub.status.busy": "2022-09-15T17:05:50.716783Z",
"iopub.status.idle": "2022-09-15T17:05:50.724355Z",
"shell.execute_reply": "2022-09-15T17:05:50.723487Z"
}
},
"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": {
"execution": {
"iopub.execute_input": "2022-09-15T17:05:50.728570Z",
"iopub.status.busy": "2022-09-15T17:05:50.728242Z",
"iopub.status.idle": "2022-09-15T17:10:20.011432Z",
"shell.execute_reply": "2022-09-15T17:10:20.010441Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] 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 17:05:50] 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 17:05:50] 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 17:05:50] 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 17:05:50] 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 17:05:50] 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 09-15 17:05:50] 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 17:05:50] 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 17:05:50] ax.service.managed_loop: Started full optimization with 30 steps.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] ax.service.managed_loop: Running optimization trial 1...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] ax.service.managed_loop: Running optimization trial 2...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] ax.service.managed_loop: Running optimization trial 3...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] ax.service.managed_loop: Running optimization trial 4...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] ax.service.managed_loop: Running optimization trial 5...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] ax.service.managed_loop: Running optimization trial 6...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] ax.service.managed_loop: Running optimization trial 7...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] ax.service.managed_loop: Running optimization trial 8...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:50] ax.service.managed_loop: Running optimization trial 9...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:51] ax.service.managed_loop: Running optimization trial 10...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:51] ax.service.managed_loop: Running optimization trial 11...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:51] ax.service.managed_loop: Running optimization trial 12...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:05:51] ax.service.managed_loop: Running optimization trial 13...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:287: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:298: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 09-15 17:06:12] ax.service.managed_loop: Running optimization trial 14...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:287: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:298: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 09-15 17:06:33] ax.service.managed_loop: Running optimization trial 15...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:287: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:298: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 09-15 17:06:54] ax.service.managed_loop: Running optimization trial 16...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:287: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:298: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 09-15 17:07:14] ax.service.managed_loop: Running optimization trial 17...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:287: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:298: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 09-15 17:07:33] ax.service.managed_loop: Running optimization trial 18...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:287: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:298: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 09-15 17:07:52] ax.service.managed_loop: Running optimization trial 19...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:287: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:08:09] ax.service.managed_loop: Running optimization trial 20...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:287: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:298: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 09-15 17:08:29] ax.service.managed_loop: Running optimization trial 21...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:287: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:298: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 09-15 17:08:50] ax.service.managed_loop: Running optimization trial 22...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:08:58] ax.service.managed_loop: Running optimization trial 23...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:09:07] ax.service.managed_loop: Running optimization trial 24...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:09:16] ax.service.managed_loop: Running optimization trial 25...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:287: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.13/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:298: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 09-15 17:09:36] ax.service.managed_loop: Running optimization trial 26...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:09:46] ax.service.managed_loop: Running optimization trial 27...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:09:53] ax.service.managed_loop: Running optimization trial 28...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:10:01] ax.service.managed_loop: Running optimization trial 29...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 09-15 17:10:10] 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": {
"execution": {
"iopub.execute_input": "2022-09-15T17:10:20.016827Z",
"iopub.status.busy": "2022-09-15T17:10:20.016500Z",
"iopub.status.idle": "2022-09-15T17:10:20.031219Z",
"shell.execute_reply": "2022-09-15T17:10:20.030305Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"{'x1': 0.2960399268816468,\n",
" 'x2': 0.051018639601891375,\n",
" 'x3': 0.4244664445819664,\n",
" 'x4': 0.31821727714367903,\n",
" 'x5': 0.2720471541434911,\n",
" 'x6': 0.5853630435103842}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_parameters"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2022-09-15T17:10:20.036839Z",
"iopub.status.busy": "2022-09-15T17:10:20.034893Z",
"iopub.status.idle": "2022-09-15T17:10:20.043971Z",
"shell.execute_reply": "2022-09-15T17:10:20.043097Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"{'hartmann6': -2.869572675007806, 'l2norm': 0.8878918208206112}"
]
},
"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": {
"execution": {
"iopub.execute_input": "2022-09-15T17:10:20.050059Z",
"iopub.status.busy": "2022-09-15T17:10:20.048363Z",
"iopub.status.idle": "2022-09-15T17:10:20.057594Z",
"shell.execute_reply": "2022-09-15T17:10:20.056324Z"
}
},
"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,
"metadata": {
"execution": {
"iopub.execute_input": "2022-09-15T17:10:20.061879Z",
"iopub.status.busy": "2022-09-15T17:10:20.061425Z",
"iopub.status.idle": "2022-09-15T17:10:21.263272Z",
"shell.execute_reply": "2022-09-15T17:10:21.262138Z"
}
},
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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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