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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": {
"execution": {
"iopub.execute_input": "2022-12-29T21:21:32.259768Z",
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"iopub.status.idle": "2022-12-29T21:21:34.931849Z",
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""
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"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:34] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n"
]
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" \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,
"execution": {
"iopub.execute_input": "2022-12-29T21:21:34.992192Z",
"iopub.status.busy": "2022-12-29T21:21:34.991316Z",
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"shell.execute_reply": "2022-12-29T21:21:34.995290Z"
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"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": "2022-12-29T21:21:34.998404Z",
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"shell.execute_reply": "2022-12-29T21:23:46.764244Z"
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{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] 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 12-29 21:21:35] 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 12-29 21:21:35] 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 12-29 21:21:35] 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 12-29 21:21:35] 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 12-29 21:21:35] 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 12-29 21:21:35] 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 12-29 21:21:35] ax.modelbridge.dispatch_utils: Calculating the number of remaining initialization trials based on num_initialization_trials=None max_initialization_trials=None num_tunable_parameters=6 num_trials=None use_batch_trials=False\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=12\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=12\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] 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 12-29 21:21:35] ax.service.managed_loop: Started full optimization with 30 steps.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 1...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/runner/work/Ax/Ax/ax/core/observation.py:274: FutureWarning:\n",
"\n",
"In a future version of pandas, a length 1 tuple will be returned when iterating over a groupby with a grouper equal to a list of length 1. Don't supply a list with a single grouper to avoid this warning.\n",
"\n",
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 2...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 3...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 4...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 5...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 6...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 7...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 8...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 9...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 10...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 11...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 12...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:35] ax.service.managed_loop: Running optimization trial 13...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:47] ax.service.managed_loop: Running optimization trial 14...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:21:54] ax.service.managed_loop: Running optimization trial 15...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:22:02] ax.service.managed_loop: Running optimization trial 16...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:22:10] ax.service.managed_loop: Running optimization trial 17...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:22:20] ax.service.managed_loop: Running optimization trial 18...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:22:28] ax.service.managed_loop: Running optimization trial 19...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:22:37] ax.service.managed_loop: Running optimization trial 20...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:22:46] ax.service.managed_loop: Running optimization trial 21...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:22:54] ax.service.managed_loop: Running optimization trial 22...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:23:01] ax.service.managed_loop: Running optimization trial 23...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:23:08] ax.service.managed_loop: Running optimization trial 24...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:23:14] ax.service.managed_loop: Running optimization trial 25...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:23:19] ax.service.managed_loop: Running optimization trial 26...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:23:25] ax.service.managed_loop: Running optimization trial 27...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:23:31] ax.service.managed_loop: Running optimization trial 28...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:23:36] ax.service.managed_loop: Running optimization trial 29...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 12-29 21:23:41] 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": {
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"outputs": [
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"text/plain": [
"{'x1': 0.15987122390002484,\n",
" 'x2': 0.16264215268809964,\n",
" 'x3': 0.6554046172897687,\n",
" 'x4': 0.3208931917266156,\n",
" 'x5': 0.28074845522590525,\n",
" 'x6': 0.727408997961325}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_parameters"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
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"outputs": [
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"data": {
"text/plain": [
"{'hartmann6': -2.808040254603555, 'l2norm': 1.0920110125619271}"
]
},
"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": {
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},
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],
"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\"."
]
},
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"Arm 0_0
hartmann6: -0.156926 (SEM: 0)
x1: 0.609558
x2: 0.38527
x3: 0.842799
x4: 0.427459
x5: 0.581037
x6: 0.242283",
"Arm 1_0
hartmann6: -0.0781471 (SEM: 0)
x1: 0.464273
x2: 0.964537
x3: 0.393806
x4: 0.741423
x5: 0.374555
x6: 0.557693",
"Arm 2_0
hartmann6: -0.950105 (SEM: 0)
x1: 0.22483
x2: 0.542636
x3: 0.93867
x4: 0.413404
x5: 0.313344
x6: 0.981889",
"Arm 3_0
hartmann6: -0.152688 (SEM: 0)
x1: 0.375896
x2: 0.167969
x3: 0.0767304
x4: 0.724087
x5: 0.508891
x6: 0.506212",
"Arm 4_0
hartmann6: -0.00463175 (SEM: 0)
x1: 0.710853
x2: 0.0418649
x3: 0.0822931
x4: 0.209533
x5: 0.854872
x6: 0.401944",
"Arm 5_0
hartmann6: -0.0786275 (SEM: 0)
x1: 0.937608
x2: 0.595109
x3: 0.26793
x4: 0.19014
x5: 0.0626795
x6: 0.885384",
"Arm 6_0
hartmann6: -0.0345872 (SEM: 0)
x1: 0.120472
x2: 0.556843
x3: 0.682256
x4: 0.928503
x5: 0.631362
x6: 0.41973",
"Arm 7_0
hartmann6: -0.0911865 (SEM: 0)
x1: 0.264624
x2: 0.279927
x3: 0.240536
x4: 0.495718
x5: 0.803813
x6: 0.602432",
"Arm 8_0
hartmann6: -0.00145489 (SEM: 0)
x1: 0.921266
x2: 0.809655
x3: 0.438727
x4: 8.80007e-05
x5: 0.744998
x6: 0.270863",
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hartmann6: -0.0146737 (SEM: 0)
x1: 0.797808
x2: 0.740205
x3: 0.187059
x4: 0.857293
x5: 0.411034
x6: 0.457282",
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hartmann6: -0.125528 (SEM: 0)
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x5: 0.10114
x6: 0.286822",
"Arm 11_0
hartmann6: -0.0366825 (SEM: 0)
x1: 0.59742
x2: 0.531002
x3: 0.554584
x4: 0.55474
x5: 0.999257
x6: 0.573779",
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hartmann6: -0.367209 (SEM: 0)
x1: 0.0703345
x2: 0.690299
x3: 0.320792
x4: 0.109058
x5: 0.0883175
x6: 0.583747",
"Arm 13_0
hartmann6: -0.954092 (SEM: 0)
x1: 0.0907955
x2: 0.619497
x3: 0.529177
x4: 0.207686
x5: 0.169786
x6: 0.809718",
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hartmann6: -0.959026 (SEM: 0)
x1: 0.0936221
x2: 0.605643
x3: 0.556463
x4: 0.22399
x5: 0.187507
x6: 0.878419",
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hartmann6: -1.11188 (SEM: 0)
x1: 0.100608
x2: 0.608034
x3: 0.611621
x4: 0.224986
x5: 0.178161
x6: 0.797704",
"Arm 16_0
hartmann6: -1.15037 (SEM: 0)
x1: 0.10625
x2: 0.604204
x3: 0.687468
x4: 0.230214
x5: 0.175157
x6: 0.753018",
"Arm 17_0
hartmann6: -0.90932 (SEM: 0)
x1: 0.114978
x2: 0.616664
x3: 0.689686
x4: 0.245888
x5: 0.111512
x6: 0.795159",
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hartmann6: -1.3647 (SEM: 0)
x1: 0.105047
x2: 0.591428
x3: 0.68324
x4: 0.230463
x5: 0.229862
x6: 0.753203",
"Arm 19_0
hartmann6: -1.5106 (SEM: 0)
x1: 0.107005
x2: 0.576046
x3: 0.695174
x4: 0.235956
x5: 0.288874
x6: 0.750303",
"Arm 20_0
hartmann6: -1.53788 (SEM: 0)
x1: 0.107604
x2: 0.564793
x3: 0.698066
x4: 0.239062
x5: 0.329937
x6: 0.751326",
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hartmann6: -1.82678 (SEM: 0)
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x2: 0.494253
x3: 0.686294
x4: 0.214039
x5: 0.318827
x6: 0.743235",
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hartmann6: -1.98481 (SEM: 0)
x1: 0.0801436
x2: 0.446914
x3: 0.691899
x4: 0.204454
x5: 0.292384
x6: 0.741138",
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hartmann6: -2.13691 (SEM: 0)
x1: 0.0678483
x2: 0.374346
x3: 0.708889
x4: 0.195153
x5: 0.285289
x6: 0.743248",
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hartmann6: -2.12357 (SEM: 0)
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x2: 0.306832
x3: 0.714573
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x5: 0.301903
x6: 0.742107",
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hartmann6: -2.37682 (SEM: 0)
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hartmann6: -2.57996 (SEM: 0)
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x2: 0.245926
x3: 0.69269
x4: 0.296408
x5: 0.292079
x6: 0.738119",
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hartmann6: -2.64922 (SEM: 0)
x1: 0.088011
x2: 0.19592
x3: 0.656921
x4: 0.342264
x5: 0.279115
x6: 0.715612",
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hartmann6: -2.80806 (SEM: 0)
x1: 0.159871
x2: 0.162642
x3: 0.655405
x4: 0.320893
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x6: 0.727409"
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"Arm 0_0
hartmann6: -0.156926 (SEM: 0)
x1: 0.609558
x2: 0.38527
x3: 0.842799
x4: 0.427459
x5: 0.581037
x6: 0.242283",
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hartmann6: -0.0781471 (SEM: 0)
x1: 0.464273
x2: 0.964537
x3: 0.393806
x4: 0.741423
x5: 0.374555
x6: 0.557693",
"Arm 2_0
hartmann6: -0.950105 (SEM: 0)
x1: 0.22483
x2: 0.542636
x3: 0.93867
x4: 0.413404
x5: 0.313344
x6: 0.981889",
"Arm 3_0
hartmann6: -0.152688 (SEM: 0)
x1: 0.375896
x2: 0.167969
x3: 0.0767304
x4: 0.724087
x5: 0.508891
x6: 0.506212",
"Arm 4_0
hartmann6: -0.00463175 (SEM: 0)
x1: 0.710853
x2: 0.0418649
x3: 0.0822931
x4: 0.209533
x5: 0.854872
x6: 0.401944",
"Arm 5_0
hartmann6: -0.0786275 (SEM: 0)
x1: 0.937608
x2: 0.595109
x3: 0.26793
x4: 0.19014
x5: 0.0626795
x6: 0.885384",
"Arm 6_0
hartmann6: -0.0345872 (SEM: 0)
x1: 0.120472
x2: 0.556843
x3: 0.682256
x4: 0.928503
x5: 0.631362
x6: 0.41973",
"Arm 7_0
hartmann6: -0.0911865 (SEM: 0)
x1: 0.264624
x2: 0.279927
x3: 0.240536
x4: 0.495718
x5: 0.803813
x6: 0.602432",
"Arm 8_0
hartmann6: -0.00145489 (SEM: 0)
x1: 0.921266
x2: 0.809655
x3: 0.438727
x4: 8.80007e-05
x5: 0.744998
x6: 0.270863",
"Arm 9_0
hartmann6: -0.0146737 (SEM: 0)
x1: 0.797808
x2: 0.740205
x3: 0.187059
x4: 0.857293
x5: 0.411034
x6: 0.457282",
"Arm 10_0
hartmann6: -0.125528 (SEM: 0)
x1: 0.173432
x2: 0.76843
x3: 0.163187
x4: 0.0888458
x5: 0.10114
x6: 0.286822",
"Arm 11_0
hartmann6: -0.0366825 (SEM: 0)
x1: 0.59742
x2: 0.531002
x3: 0.554584
x4: 0.55474
x5: 0.999257
x6: 0.573779",
"Arm 12_0
hartmann6: -0.367209 (SEM: 0)
x1: 0.0703345
x2: 0.690299
x3: 0.320792
x4: 0.109058
x5: 0.0883175
x6: 0.583747",
"Arm 13_0
hartmann6: -0.954092 (SEM: 0)
x1: 0.0907955
x2: 0.619497
x3: 0.529177
x4: 0.207686
x5: 0.169786
x6: 0.809718",
"Arm 14_0
hartmann6: -0.959026 (SEM: 0)
x1: 0.0936221
x2: 0.605643
x3: 0.556463
x4: 0.22399
x5: 0.187507
x6: 0.878419",
"Arm 15_0
hartmann6: -1.11188 (SEM: 0)
x1: 0.100608
x2: 0.608034
x3: 0.611621
x4: 0.224986
x5: 0.178161
x6: 0.797704",
"Arm 16_0
hartmann6: -1.15037 (SEM: 0)
x1: 0.10625
x2: 0.604204
x3: 0.687468
x4: 0.230214
x5: 0.175157
x6: 0.753018",
"Arm 17_0
hartmann6: -0.90932 (SEM: 0)
x1: 0.114978
x2: 0.616664
x3: 0.689686
x4: 0.245888
x5: 0.111512
x6: 0.795159",
"Arm 18_0
hartmann6: -1.3647 (SEM: 0)
x1: 0.105047
x2: 0.591428
x3: 0.68324
x4: 0.230463
x5: 0.229862
x6: 0.753203",
"Arm 19_0
hartmann6: -1.5106 (SEM: 0)
x1: 0.107005
x2: 0.576046
x3: 0.695174
x4: 0.235956
x5: 0.288874
x6: 0.750303",
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hartmann6: -1.53788 (SEM: 0)
x1: 0.107604
x2: 0.564793
x3: 0.698066
x4: 0.239062
x5: 0.329937
x6: 0.751326",
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hartmann6: -1.82678 (SEM: 0)
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x5: 0.318827
x6: 0.743235",
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hartmann6: -1.98481 (SEM: 0)
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x2: 0.446914
x3: 0.691899
x4: 0.204454
x5: 0.292384
x6: 0.741138",
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hartmann6: -2.13691 (SEM: 0)
x1: 0.0678483
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x4: 0.195153
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x6: 0.743248",
"Arm 24_0
hartmann6: -2.12357 (SEM: 0)
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x3: 0.714573
x4: 0.16544
x5: 0.301903
x6: 0.742107",
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hartmann6: -2.37682 (SEM: 0)
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x4: 0.245628
x5: 0.288675
x6: 0.749132",
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hartmann6: -2.57996 (SEM: 0)
x1: 0.0839778
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x6: 0.738119",
"Arm 27_0
hartmann6: -2.64922 (SEM: 0)
x1: 0.088011
x2: 0.19592
x3: 0.656921
x4: 0.342264
x5: 0.279115
x6: 0.715612",
"Arm 28_0
hartmann6: -2.80806 (SEM: 0)
x1: 0.159871
x2: 0.162642
x3: 0.655405
x4: 0.320893
x5: 0.280748
x6: 0.727409"
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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",
" ylabel=\"Hartmann6\",\n",
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