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"cells": [
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"cell_type": "markdown",
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"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"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:37] 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 04-25 21:18:37] 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 21:18:37] 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 21:18:37] 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 21:18:37] 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 21:18:37] 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 21:18:37] 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 04-25 21:18:37] 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 21:18:37] 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 04-25 21:18:37] ax.service.managed_loop: Started full optimization with 30 steps.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:37] ax.service.managed_loop: Running optimization trial 1...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:37] ax.service.managed_loop: Running optimization trial 2...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:37] ax.service.managed_loop: Running optimization trial 3...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:37] ax.service.managed_loop: Running optimization trial 4...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:37] ax.service.managed_loop: Running optimization trial 5...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:38] ax.service.managed_loop: Running optimization trial 6...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:38] ax.service.managed_loop: Running optimization trial 7...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:38] ax.service.managed_loop: Running optimization trial 8...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:38] ax.service.managed_loop: Running optimization trial 9...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:38] ax.service.managed_loop: Running optimization trial 10...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:38] ax.service.managed_loop: Running optimization trial 11...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:38] ax.service.managed_loop: Running optimization trial 12...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:38] ax.service.managed_loop: Running optimization trial 13...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.7.12/x64/lib/python3.7/site-packages/gpytorch/lazy/lazy_tensor.py:1741: UserWarning:\n",
"\n",
"torch.triangular_solve is deprecated in favor of torch.linalg.solve_triangularand will be removed in a future PyTorch release.\n",
"torch.linalg.solve_triangular has its arguments reversed and does not return a copy of one of the inputs.\n",
"X = torch.triangular_solve(B, A).solution\n",
"should be replaced with\n",
"X = torch.linalg.solve_triangular(A, B). (Triggered internally at ../aten/src/ATen/native/BatchLinearAlgebra.cpp:1672.)\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:44] ax.service.managed_loop: Running optimization trial 14...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:50] ax.service.managed_loop: Running optimization trial 15...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:18:57] ax.service.managed_loop: Running optimization trial 16...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:19:02] ax.service.managed_loop: Running optimization trial 17...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:19:08] ax.service.managed_loop: Running optimization trial 18...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:19:14] ax.service.managed_loop: Running optimization trial 19...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:19:20] ax.service.managed_loop: Running optimization trial 20...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:19:26] ax.service.managed_loop: Running optimization trial 21...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:19:31] ax.service.managed_loop: Running optimization trial 22...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:19:37] ax.service.managed_loop: Running optimization trial 23...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:19:42] ax.service.managed_loop: Running optimization trial 24...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:19:48] ax.service.managed_loop: Running optimization trial 25...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:19:54] ax.service.managed_loop: Running optimization trial 26...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:20:00] ax.service.managed_loop: Running optimization trial 27...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:20:04] ax.service.managed_loop: Running optimization trial 28...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:20:09] ax.service.managed_loop: Running optimization trial 29...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-25 21:20:13] 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': 0.22637613467008277,\n",
" 'x2': 0.07548106422379,\n",
" 'x3': 0.5462105765393369,\n",
" 'x4': 0.24757068559356862,\n",
" 'x5': 0.3199846305494837,\n",
" 'x6': 0.6463687042752487}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_parameters"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'l2norm': 0.9678762491691202, 'hartmann6': -3.1728447965223836}"
]
},
"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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"Arm 0_0
hartmann6: -0.242245 (SEM: 0)
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x6: 0.0620148",
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hartmann6: -0.253544 (SEM: 0)
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"Arm 2_0
hartmann6: -0.217305 (SEM: 0)
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x6: 0.642009",
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hartmann6: -0.267878 (SEM: 0)
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hartmann6: -0.00238585 (SEM: 0)
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x6: 0.955021",
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hartmann6: -0.0945877 (SEM: 0)
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x5: 0.323338
x6: 0.582829",
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x6: 0.377394",
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x5: 0.0717724
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x5: 0.143763
x6: 0.774094",
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hartmann6: -1.49377 (SEM: 0)
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x5: 0.167834
x6: 0.779717",
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hartmann6: -1.62365 (SEM: 0)
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x6: 0.791011",
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hartmann6: -1.69943 (SEM: 0)
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x6: 0.846738",
"Arm 17_0
hartmann6: -2.17145 (SEM: 0)
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x6: 0.789028",
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hartmann6: -2.48092 (SEM: 0)
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hartmann6: -2.55046 (SEM: 0)
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hartmann6: -3.11298 (SEM: 0)
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"Arm 28_0
hartmann6: -3.17288 (SEM: 0)
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hartmann6: -0.242245 (SEM: 0)
x1: 0.39217
x2: 0.341914
x3: 0.159259
x4: 0.437701
x5: 0.745598
x6: 0.0620148",
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hartmann6: -0.253544 (SEM: 0)
x1: 0.663238
x2: 0.714569
x3: 0.588652
x4: 0.27768
x5: 0.139057
x6: 0.271218",
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hartmann6: -0.217305 (SEM: 0)
x1: 0.846448
x2: 0.217095
x3: 0.348404
x4: 0.671583
x5: 0.339592
x6: 0.642009",
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hartmann6: -0.267878 (SEM: 0)
x1: 0.916066
x2: 0.321183
x3: 0.137546
x4: 0.505969
x5: 0.415414
x6: 0.525829",
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hartmann6: -0.258422 (SEM: 0)
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x2: 0.364805
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x4: 0.273991
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x6: 0.978689",
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hartmann6: -1.23921 (SEM: 0)
x1: 0.0702075
x2: 0.223758
x3: 0.719703
x4: 0.460041
x5: 0.11914
x6: 0.769392",
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hartmann6: -0.184271 (SEM: 0)
x1: 0.617574
x2: 0.465144
x3: 0.645355
x4: 0.766496
x5: 0.14884
x6: 0.638048",
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hartmann6: -0.00238585 (SEM: 0)
x1: 0.224609
x2: 0.968628
x3: 0.492947
x4: 0.925068
x5: 0.883348
x6: 0.955021",
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hartmann6: -0.0945877 (SEM: 0)
x1: 0.579061
x2: 0.691852
x3: 0.901277
x4: 0.752974
x5: 0.323338
x6: 0.582829",
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hartmann6: -0.0220674 (SEM: 0)
x1: 0.891122
x2: 0.601659
x3: 0.468342
x4: 0.305274
x5: 0.460138
x6: 0.0038387",
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hartmann6: -0.0186132 (SEM: 0)
x1: 0.872585
x2: 0.845563
x3: 0.760308
x4: 0.638518
x5: 0.535373
x6: 0.419434",
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hartmann6: -0.107191 (SEM: 0)
x1: 0.989513
x2: 0.317229
x3: 0.648857
x4: 0.558124
x5: 0.306877
x6: 0.377394",
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hartmann6: -0.921573 (SEM: 0)
x1: 0.00618232
x2: 0.168376
x3: 0.728567
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x5: 0.0717724
x6: 0.765224",
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hartmann6: -1.38199 (SEM: 0)
x1: 0.109789
x2: 0.262375
x3: 0.725919
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x5: 0.143763
x6: 0.774094",
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hartmann6: -1.49377 (SEM: 0)
x1: 0.155198
x2: 0.294492
x3: 0.71667
x4: 0.48058
x5: 0.167834
x6: 0.779717",
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x1: 0.205499
x2: 0.291081
x3: 0.654117
x4: 0.467266
x5: 0.181966
x6: 0.791011",
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hartmann6: -1.69943 (SEM: 0)
x1: 0.249338
x2: 0.277159
x3: 0.634864
x4: 0.426423
x5: 0.185014
x6: 0.846738",
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hartmann6: -2.17145 (SEM: 0)
x1: 0.265776
x2: 0.231359
x3: 0.645915
x4: 0.379026
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x6: 0.789028",
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hartmann6: -2.48092 (SEM: 0)
x1: 0.300595
x2: 0.203987
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x4: 0.334825
x5: 0.246681
x6: 0.751305",
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hartmann6: -2.55046 (SEM: 0)
x1: 0.323006
x2: 0.16023
x3: 0.71443
x4: 0.285792
x5: 0.268074
x6: 0.718299",
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x1: 0.305742
x2: 0.258394
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x4: 0.24972
x5: 0.261953
x6: 0.71249",
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hartmann6: -2.59462 (SEM: 0)
x1: 0.275908
x2: 0.191027
x3: 0.726008
x4: 0.279843
x5: 0.320087
x6: 0.7388",
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hartmann6: -2.60407 (SEM: 0)
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x2: 0.200396
x3: 0.670185
x4: 0.272081
x5: 0.345044
x6: 0.741917",
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hartmann6: -2.30369 (SEM: 0)
x1: 0.345553
x2: 0.203027
x3: 0.755474
x4: 0.263989
x5: 0.333498
x6: 0.765127",
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hartmann6: -2.90431 (SEM: 0)
x1: 0.268276
x2: 0.164962
x3: 0.655735
x4: 0.26826
x5: 0.329887
x6: 0.691725",
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x1: 0.230964
x2: 0.137343
x3: 0.609254
x4: 0.258392
x5: 0.333731
x6: 0.628885",
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x1: 0.2008
x2: 0.114854
x3: 0.569471
x4: 0.213204
x5: 0.318605
x6: 0.644291",
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x1: 0.171268
x2: 0.170045
x3: 0.585367
x4: 0.200932
x5: 0.317134
x6: 0.606951",
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x1: 0.226376
x2: 0.0754811
x3: 0.546211
x4: 0.247571
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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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"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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