{ "cells": [ { "cell_type": "markdown", "metadata": { "originalKey": "e23719d9-8a24-4208-8439-34e7b8270c79" }, "source": [ "# Visualizations\n", "\n", "This tutorial illustrates the core visualization utilities available in Ax." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2022-12-29T21:28:36.129950Z", "iopub.status.busy": "2022-12-29T21:28:36.129578Z", "iopub.status.idle": "2022-12-29T21:28:38.405539Z", "shell.execute_reply": "2022-12-29T21:28:38.404678Z" }, "executionStartTime": 1627652821316, "executionStopTime": 1627652822868, "hidden_ranges": [], "originalKey": "101b0e96-5b3d-48c5-bf3c-677b4ddf90c7", "requestMsgId": "c0dd9aaf-896d-4ea9-912f-1e58d301d114" }, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] 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", "from ax.service.ax_client import AxClient, ObjectiveProperties\n", "\n", "from ax.modelbridge.cross_validation import cross_validate\n", "from ax.plot.contour import interact_contour\n", "from ax.plot.diagnostic import interact_cross_validation\n", "from ax.plot.scatter import(\n", " interact_fitted,\n", " plot_objective_vs_constraints,\n", " tile_fitted,\n", ")\n", "from ax.plot.slice import plot_slice\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": { "code_folding": [], "hidden_ranges": [], "originalKey": "8449378f-890e-4e76-8d73-ce2aa4120a69", "showInput": true }, "source": [ "## 1. Create experiment and run optimization\n", "\n", "The vizualizations require an experiment object and a model fit on the evaluated data. The routine below is a copy of the Service API tutorial, so the explanation here is omitted. Retrieving the experiment and model objects for each API paradigm is shown in the respective tutorials" ] }, { "cell_type": "markdown", "metadata": { "originalKey": "f7544e06-6c6a-4841-b659-3be6a198a948" }, "source": [ "#### 1a. Define search space and evaluation function" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2022-12-29T21:28:38.466808Z", "iopub.status.busy": "2022-12-29T21:28:38.465950Z", "iopub.status.idle": "2022-12-29T21:28:38.472423Z", "shell.execute_reply": "2022-12-29T21:28:38.470765Z" }, "executionStartTime": 1627652824829, "executionStopTime": 1627652824877, "hidden_ranges": [], "originalKey": "28f6cb76-828f-445d-bdda-ba057c87dcd0", "requestMsgId": "7495e7e2-1025-4292-b3aa-e953739cef3e" }, "outputs": [], "source": [ "noise_sd = 0.1\n", "param_names = [f\"x{i+1}\" for i in range(6)] # x1, x2, ..., x6\n", "\n", "def noisy_hartmann_evaluation_function(parameterization):\n", " x = np.array([parameterization.get(p_name) for p_name in param_names])\n", " noise1, noise2 = np.random.normal(0, noise_sd, 2)\n", "\n", " return {\n", " \"hartmann6\": (hartmann6(x) + noise1, noise_sd),\n", " \"l2norm\": (np.sqrt((x ** 2).sum()) + noise2, noise_sd)\n", " }\n" ] }, { "cell_type": "markdown", "metadata": { "originalKey": "17a51543-298e-47d4-bcd9-33459fe1169e" }, "source": [ "#### 1b. Create Experiment" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2022-12-29T21:28:38.474912Z", "iopub.status.busy": "2022-12-29T21:28:38.474328Z", "iopub.status.idle": "2022-12-29T21:28:38.486766Z", "shell.execute_reply": "2022-12-29T21:28:38.485961Z" }, "executionStartTime": 1627654956712, "executionStopTime": 1627654956823, "hidden_ranges": [], "originalKey": "6fca889c-a4ff-42ef-a669-6eb8803de89c", "requestMsgId": "905eff52-e649-4bd5-abf0-ff69c1549852" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Starting optimization with verbose logging. To disable logging, set the `verbose_logging` argument to `False`. Note that float values in the logs are rounded to 6 decimal points.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. 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 21:28:38] 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 21:28:38] 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 21:28:38] 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 21:28:38] 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 21:28:38] 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 21:28:38] 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=[]).\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] 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 21:28:38] 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 21:28:38] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=12\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=12\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] 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" ] } ], "source": [ "ax_client = AxClient()\n", "ax_client.create_experiment(\n", " name=\"test_visualizations\",\n", " parameters=[\n", " {\n", " \"name\": p_name,\n", " \"type\": \"range\",\n", " \"bounds\": [0.0, 1.0],\n", " }\n", " for p_name in param_names\n", " ],\n", " objectives={\"hartmann6\": ObjectiveProperties(minimize=True)},\n", " outcome_constraints=[\"l2norm <= 1.25\"]\n", ")" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ab892f7c-4830-4c1d-b476-ec1078ec3faf", "showInput": false }, "source": [ "#### 1c. Run the optimization and fit a GP on all data" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2022-12-29T21:28:38.489232Z", "iopub.status.busy": "2022-12-29T21:28:38.488620Z", "iopub.status.idle": "2022-12-29T21:30:50.353812Z", "shell.execute_reply": "2022-12-29T21:30:50.353284Z" }, "executionStartTime": 1627654642967, "executionStopTime": 1627654862819, "hidden_ranges": [], "originalKey": "7269a5ba-45c8-4acf-ac83-a5ea8a52d6c1", "requestMsgId": "c7a4dea8-fd6d-4e1a-84de-ad973ede0cd7" }, "outputs": [ { "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" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.509467, 'x2': 0.028962, 'x3': 0.919525, 'x4': 0.718578, 'x5': 0.205345, 'x6': 0.74537}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.294883, 0.1), 'l2norm': (1.540891, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.030807, 'x2': 0.733315, 'x3': 0.805419, 'x4': 0.732529, 'x5': 0.226611, 'x6': 0.99587}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.335388, 0.1), 'l2norm': (1.784087, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.544919, 'x2': 0.9505, 'x3': 0.93452, 'x4': 0.003054, 'x5': 0.693434, 'x6': 0.049953}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (0.070062, 0.1), 'l2norm': (1.534787, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.458143, 'x2': 0.862874, 'x3': 0.585976, 'x4': 0.042028, 'x5': 0.928453, 'x6': 0.167484}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.204773, 0.1), 'l2norm': (1.505643, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.854988, 'x2': 0.117923, 'x3': 0.417829, 'x4': 0.588809, 'x5': 0.235495, 'x6': 0.00535}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.101418, 0.1), 'l2norm': (1.122423, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.060659, 'x2': 0.36236, 'x3': 0.698587, 'x4': 0.533907, 'x5': 0.162588, 'x6': 0.22702}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.089756, 0.1), 'l2norm': (1.01303, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.681922, 'x2': 0.045512, 'x3': 0.276457, 'x4': 0.682553, 'x5': 0.888026, 'x6': 0.926312}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.014906, 0.1), 'l2norm': (1.499251, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.643002, 'x2': 0.806809, 'x3': 0.602528, 'x4': 0.542176, 'x5': 0.873224, 'x6': 0.263903}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.550204, 0.1), 'l2norm': (1.614762, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.438348, 'x2': 0.01965, 'x3': 0.225021, 'x4': 0.70105, 'x5': 0.820094, 'x6': 0.747691}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (0.022785, 0.1), 'l2norm': (1.46755, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.334092, 'x2': 0.049544, 'x3': 0.31188, 'x4': 0.561487, 'x5': 0.623716, 'x6': 0.951681}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.065793, 0.1), 'l2norm': (1.22676, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.013929, 'x2': 0.867573, 'x3': 0.524857, 'x4': 0.61982, 'x5': 0.352199, 'x6': 0.357934}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-0.226878, 0.1), 'l2norm': (1.236159, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.10638, 'x2': 0.925673, 'x3': 0.347194, 'x4': 0.73536, 'x5': 0.144307, 'x6': 0.885829}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:38] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.025526, 0.1), 'l2norm': (1.622494, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:51] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.289555, 'x2': 0.68663, 'x3': 0.616159, 'x4': 0.595965, 'x5': 0.395963, 'x6': 0.235655}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:28:51] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.094233, 0.1), 'l2norm': (1.210456, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:29:13] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.2114, 'x2': 0.659825, 'x3': 0.629484, 'x4': 0.576865, 'x5': 0.256249, 'x6': 0.226572}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:29:13] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-0.771727, 0.1), 'l2norm': (1.092837, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:29:40] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.383577, 'x2': 0.690274, 'x3': 0.614337, 'x4': 0.612205, 'x5': 0.333837, 'x6': 0.169309}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:29:40] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.958704, 0.1), 'l2norm': (1.137047, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:29:54] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.411374, 'x2': 0.657816, 'x3': 0.611819, 'x4': 0.603055, 'x5': 0.245093, 'x6': 0.163786}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:29:54] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.631368, 0.1), 'l2norm': (1.141971, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:30:03] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.401157, 'x2': 0.728809, 'x3': 0.619218, 'x4': 0.636153, 'x5': 0.338858, 'x6': 0.118562}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:30:03] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-2.245452, 0.1), 'l2norm': (1.219328, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:30:16] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.433516, 'x2': 0.73424, 'x3': 0.550635, 'x4': 0.632669, 'x5': 0.363638, 'x6': 0.11215}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:30:16] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-2.313931, 0.1), 'l2norm': (1.463567, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:30:34] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.422282, 'x2': 0.697169, 'x3': 0.68871, 'x4': 0.623526, 'x5': 0.330549, 'x6': 0.108302}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:30:34] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.171868, 0.1), 'l2norm': (1.329198, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:30:50] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.405729, 'x2': 0.686861, 'x3': 0.567166, 'x4': 0.646465, 'x5': 0.268599, 'x6': 0.113926}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:30:50] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.101002, 0.1), 'l2norm': (1.257834, 0.1)}.\n" ] } ], "source": [ "for i in range(20):\n", " parameters, trial_index = ax_client.get_next_trial()\n", " # Local evaluation here can be replaced with deployment to external system.\n", " ax_client.complete_trial(trial_index=trial_index, raw_data=noisy_hartmann_evaluation_function(parameters))" ] }, { "cell_type": "markdown", "metadata": { "originalKey": "72f4d3e7-fa04-43d0-8451-ded292e705df" }, "source": [ "## 2. Contour plots\n", "\n", "The plot below shows the response surface for `hartmann6` metric as a function of the `x1`, `x2` parameters.\n", "\n", "The other parameters are fixed in the middle of their respective ranges, which in this example is 0.5 for all of them." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2022-12-29T21:30:50.357615Z", "iopub.status.busy": "2022-12-29T21:30:50.356455Z", "iopub.status.idle": "2022-12-29T21:30:50.976990Z", "shell.execute_reply": "2022-12-29T21:30:50.976433Z" }, "executionStartTime": 1627654870209, "executionStopTime": 1627654871972, "hidden_ranges": [], "originalKey": "843df85c-965d-4a83-9fe1-696225d81c0f", "requestMsgId": "4a643541-867c-46b6-868d-64337920c2a3" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-29 21:30:50] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Remaining parameters are affixed to the middle of their range.\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "autocolorscale": false, "autocontour": true, "colorbar": { "tickfont": { "size": 8 }, "ticksuffix": "", "x": 0.45, "y": 0.5 }, "colorscale": [ [ 0.0, "rgb(247,252,253)" ], [ 0.125, "rgb(229,245,249)" ], [ 0.25, "rgb(204,236,230)" ], [ 0.375, "rgb(153,216,201)" ], [ 0.5, "rgb(102,194,164)" ], [ 0.625, "rgb(65,174,118)" ], [ 0.75, "rgb(35,139,69)" ], [ 0.875, "rgb(0,109,44)" ], [ 1.0, "rgb(0,68,27)" ] ], "contours": { "coloring": "heatmap" }, "hoverinfo": "x+y+z", "ncontours": 25, "type": "contour", "x": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# this could alternately be done with `ax.plot.contour.plot_contour`\n", "render(ax_client.get_contour_plot(param_x=\"x1\", param_y=\"x2\", metric_name='hartmann6'))" ] }, { "cell_type": "markdown", "metadata": { "originalKey": "1de0991a-d99b-4d07-acec-4a2eb4a20a73" }, "source": [ "#### 2a. Interactive contour plot\n", "\n", "The plot below allows toggling between different pairs of parameters to view the contours." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2022-12-29T21:30:50.984171Z", "iopub.status.busy": "2022-12-29T21:30:50.983532Z", "iopub.status.idle": "2022-12-29T21:31:05.320688Z", "shell.execute_reply": "2022-12-29T21:31:05.320071Z" }, "executionStartTime": 1627652959076, "executionStopTime": 1627652982911, "hidden_ranges": [], "originalKey": "4af9f166-0163-4ff5-9ecb-f534a69efe3d", "requestMsgId": "2de6919e-92e1-4425-8d90-b117e9f41855" }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "autocolorscale": false, "autocontour": true, "colorbar": { "len": 0.875, "tickfont": { "size": 8 }, "ticksuffix": "", "x": 0.45, "y": 0.5 }, "colorscale": [ [ 0.0, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model = ax_client.generation_strategy.model\n", "render(interact_contour(model=model, metric_name='hartmann6'))" ] }, { "cell_type": "markdown", "metadata": { "originalKey": "1ff470bb-5daf-4179-b814-01cc80dafe3e" }, "source": [ "## 3. Tradeoff plots\n", "This plot illustrates the tradeoffs achievable for 2 different metrics. The plot takes the x-axis metric as input (usually the objective) and allows toggling among all other metrics for the y-axis.\n", "\n", "This is useful to get a sense of the pareto frontier (i.e. what is the best objective value achievable for different bounds on the constraint)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2022-12-29T21:31:05.530261Z", "iopub.status.busy": "2022-12-29T21:31:05.529568Z", "iopub.status.idle": "2022-12-29T21:31:05.676940Z", "shell.execute_reply": "2022-12-29T21:31:05.676330Z" }, "executionStartTime": 1627652996903, "executionStopTime": 1627652997294, "originalKey": "57023556-0293-44ef-91d6-81b911ff41d3", "requestMsgId": "10b72ecc-a019-42a1-8358-18f14927ef75" }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "error_x": { "array": [ 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "error_y": { "array": [ 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "hoverinfo": "text", "marker": { "color": "rgba(128,177,211,1)" }, "mode": "markers", "name": "In-sample", "showlegend": true, "text": [ "Arm 0_0

hartmann6: -0.295 [-0.491, -0.099]
l2norm: 1.541 [1.345, 1.737]

Parameterization:
x1: 0.5094669461250305
x2: 0.028961949050426483
x3: 0.9195249676704407
x4: 0.7185776829719543
x5: 0.20534470677375793
x6: 0.7453696727752686", "Arm 1_0

hartmann6: -0.335 [-0.531, -0.139]
l2norm: 1.784 [1.588, 1.980]

Parameterization:
x1: 0.030807215720415115
x2: 0.7333147255703807
x3: 0.8054188275709748
x4: 0.7325294045731425
x5: 0.22661086171865463
x6: 0.9958701143041253", "Arm 2_0

hartmann6: 0.07 [-0.126, 0.266]
l2norm: 1.535 [1.339, 1.731]

Parameterization:
x1: 0.5449186321347952
x2: 0.9504998587071896
x3: 0.9345201617106795
x4: 0.003054482862353325
x5: 0.6934341117739677
x6: 0.049952831119298935", "Arm 3_0

hartmann6: -0.205 [-0.401, -0.009]
l2norm: 1.506 [1.310, 1.702]

Parameterization:
x1: 0.4581432929262519
x2: 0.8628739174455404
x3: 0.585976418107748
x4: 0.04202813468873501
x5: 0.9284532889723778
x6: 0.16748409066349268", "Arm 4_0

hartmann6: -0.101 [-0.297, 0.095]
l2norm: 1.122 [0.926, 1.318]

Parameterization:
x1: 0.8549876464530826
x2: 0.11792286671698093
x3: 0.4178288094699383
x4: 0.5888091530650854
x5: 0.23549478594213724
x6: 0.005349679850041866", "Arm 5_0

hartmann6: -0.09 [-0.286, 0.106]
l2norm: 1.013 [0.817, 1.209]

Parameterization:
x1: 0.060659466311335564
x2: 0.36236009281128645
x3: 0.6985868457704782
x4: 0.5339070362970233
x5: 0.16258792020380497
x6: 0.22701952792704105", "Arm 6_0

hartmann6: -0.015 [-0.211, 0.181]
l2norm: 1.499 [1.303, 1.695]

Parameterization:
x1: 0.6819224553182721
x2: 0.0455122971907258
x3: 0.27645703963935375
x4: 0.682553194463253
x5: 0.8880256414413452
x6: 0.9263124475255609", "Arm 7_0

hartmann6: -0.55 [-0.746, -0.354]
l2norm: 1.615 [1.419, 1.811]

Parameterization:
x1: 0.6430023284628987
x2: 0.8068088106811047
x3: 0.6025278307497501
x4: 0.5421762457117438
x5: 0.8732241541147232
x6: 0.26390309911221266", "Arm 8_0

hartmann6: 0.023 [-0.173, 0.219]
l2norm: 1.468 [1.272, 1.664]

Parameterization:
x1: 0.43834762647747993
x2: 0.01964978128671646
x3: 0.22502082213759422
x4: 0.7010497134178877
x5: 0.8200943367555737
x6: 0.7476914403960109", "Arm 9_0

hartmann6: -0.066 [-0.262, 0.130]
l2norm: 1.227 [1.031, 1.423]

Parameterization:
x1: 0.33409237023442984
x2: 0.04954400472342968
x3: 0.3118802411481738
x4: 0.5614874539896846
x5: 0.6237162770703435
x6: 0.9516805456951261", "Arm 10_0

hartmann6: -0.227 [-0.423, -0.031]
l2norm: 1.236 [1.040, 1.432]

Parameterization:
x1: 0.013928516767919064
x2: 0.8675733413547277
x3: 0.5248574297875166
x4: 0.6198204094544053
x5: 0.3521989854052663
x6: 0.35793409403413534", "Arm 11_0

hartmann6: -0.026 [-0.222, 0.170]
l2norm: 1.622 [1.426, 1.818]

Parameterization:
x1: 0.10638012737035751
x2: 0.9256733832880855
x3: 0.3471939144656062
x4: 0.7353604743257165
x5: 0.14430653676390648
x6: 0.8858285704627633", "Arm 12_0

hartmann6: -1.094 [-1.290, -0.898]
l2norm: 1.21 [1.014, 1.406]

Parameterization:
x1: 0.28955512219069973
x2: 0.6866303111729859
x3: 0.6161594597767127
x4: 0.5959654157152262
x5: 0.3959626615886123
x6: 0.23565533436845468", "Arm 13_0

hartmann6: -0.772 [-0.968, -0.576]
l2norm: 1.093 [0.897, 1.289]

Parameterization:
x1: 0.2114001689955874
x2: 0.6598251673457936
x3: 0.629483578828031
x4: 0.5768654723129062
x5: 0.2562493443252856
x6: 0.22657214115599586", "Arm 14_0

hartmann6: -1.959 [-2.155, -1.763]
l2norm: 1.137 [0.941, 1.333]

Parameterization:
x1: 0.3835770872100636
x2: 0.6902736821080439
x3: 0.614336939034702
x4: 0.612204582470053
x5: 0.3338366081900223
x6: 0.16930900485726838", "Arm 15_0

hartmann6: -1.631 [-1.827, -1.435]
l2norm: 1.142 [0.946, 1.338]

Parameterization:
x1: 0.4113735568794019
x2: 0.6578164344992266
x3: 0.6118187105656752
x4: 0.6030546811245218
x5: 0.24509284301974327
x6: 0.16378593941080893", "Arm 16_0

hartmann6: -2.245 [-2.441, -2.049]
l2norm: 1.219 [1.023, 1.415]

Parameterization:
x1: 0.4011566789789615
x2: 0.7288091274911536
x3: 0.6192184099313921
x4: 0.6361527822996007
x5: 0.3388579795862753
x6: 0.11856189457534973", "Arm 17_0

hartmann6: -2.314 [-2.510, -2.118]
l2norm: 1.464 [1.268, 1.660]

Parameterization:
x1: 0.43351642045594785
x2: 0.7342402117013916
x3: 0.5506345147574029
x4: 0.6326688218781511
x5: 0.36363810803812213
x6: 0.11214964609541407", "Arm 18_0

hartmann6: -2.172 [-2.368, -1.976]
l2norm: 1.329 [1.133, 1.525]

Parameterization:
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x2: 0.6971691688844808
x3: 0.6887101325469829
x4: 0.6235261603801038
x5: 0.3305488294966215
x6: 0.10830150156449667" ], "type": "scatter", "visible": false, "x": [ -0.29488302632117913, -0.33538795600378873, 0.0700617460612015, -0.2047730553594639, -0.1014182831805625, -0.0897555178016686, -0.014906310802734815, -0.5502040419982255, 0.022785079517198957, -0.06579347122370713, -0.22687761568544357, -0.025526049429322177, -1.0942332365637268, -0.7717271086377415, -1.9587035805324782, -1.6313683989257122, -2.2454523792942007, -2.313930803845192, -2.1718678112421244 ], "y": [ 1.540891301510101, 1.784087313450029, 1.534787228368841, 1.5056426174057556, 1.1224233900647862, 1.0130303221267658, 1.499250878657248, 1.6147618494568816, 1.4675495105439027, 1.2267603401526384, 1.2361587110258938, 1.6224940867238529, 1.2104556932471395, 1.0928373677503216, 1.1370471525753243, 1.141971020576065, 1.219327749244669, 1.4635667930128662, 1.3291978604406216 ] }, { "error_x": { "array": [ 0.1932781562448292, 0.19285414767110415, 0.19279347565911162, 0.19274264378496445, 0.19329351497426547, 0.19249911440604092, 0.19263854548408707, 0.193142532330463, 0.19243629233746398, 0.19278274279903154, 0.19251975141504468, 0.19285104089627028, 0.1809842771694597, 0.18486479035159853, 0.14529689078665273, 0.17695140312915558, 0.13589681666029446, 0.16780132817772844, 0.16622335475067074 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "error_y": { "array": [ 0.17526162745920226, 0.17322513970655232, 0.1729772074841761, 0.17211754231401005, 0.17487072358376848, 0.16770082146930093, 0.16742351543795805, 0.17373965003431174, 0.16641505780387225, 0.17055259232106876, 0.16663433614395523, 0.17325009772429908, 0.1331133351159286, 0.13115801584838727, 0.08916358008277454, 0.12362436897297399, 0.09676526872091194, 0.12166410931068118, 0.11804321047435673 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "hoverinfo": "text", "marker": { "color": "rgba(128,177,211,1)" }, "mode": "markers", "name": "In-sample", "showlegend": true, "text": [ "Arm 0_0

hartmann6: -0.294 [-0.487, -0.100]
l2norm: 1.516 [1.341, 1.691]

Parameterization:
x1: 0.5094669461250305
x2: 0.028961949050426483
x3: 0.9195249676704407
x4: 0.7185776829719543
x5: 0.20534470677375793
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hartmann6: -0.331 [-0.523, -0.138]
l2norm: 1.719 [1.546, 1.892]

Parameterization:
x1: 0.030807215720415115
x2: 0.7333147255703807
x3: 0.8054188275709748
x4: 0.7325294045731425
x5: 0.22661086171865463
x6: 0.9958701143041253", "Arm 2_0

hartmann6: 0.058 [-0.135, 0.250]
l2norm: 1.517 [1.344, 1.690]

Parameterization:
x1: 0.5449186321347952
x2: 0.9504998587071896
x3: 0.9345201617106795
x4: 0.003054482862353325
x5: 0.6934341117739677
x6: 0.049952831119298935", "Arm 3_0

hartmann6: -0.204 [-0.397, -0.011]
l2norm: 1.504 [1.331, 1.676]

Parameterization:
x1: 0.4581432929262519
x2: 0.8628739174455404
x3: 0.585976418107748
x4: 0.04202813468873501
x5: 0.9284532889723778
x6: 0.16748409066349268", "Arm 4_0

hartmann6: -0.11 [-0.303, 0.084]
l2norm: 1.179 [1.004, 1.354]

Parameterization:
x1: 0.8549876464530826
x2: 0.11792286671698093
x3: 0.4178288094699383
x4: 0.5888091530650854
x5: 0.23549478594213724
x6: 0.005349679850041866", "Arm 5_0

hartmann6: -0.098 [-0.291, 0.094]
l2norm: 1.072 [0.904, 1.240]

Parameterization:
x1: 0.060659466311335564
x2: 0.36236009281128645
x3: 0.6985868457704782
x4: 0.5339070362970233
x5: 0.16258792020380497
x6: 0.22701952792704105", "Arm 6_0

hartmann6: -0.019 [-0.212, 0.173]
l2norm: 1.475 [1.308, 1.643]

Parameterization:
x1: 0.6819224553182721
x2: 0.0455122971907258
x3: 0.27645703963935375
x4: 0.682553194463253
x5: 0.8880256414413452
x6: 0.9263124475255609", "Arm 7_0

hartmann6: -0.55 [-0.743, -0.357]
l2norm: 1.579 [1.406, 1.753]

Parameterization:
x1: 0.6430023284628987
x2: 0.8068088106811047
x3: 0.6025278307497501
x4: 0.5421762457117438
x5: 0.8732241541147232
x6: 0.26390309911221266", "Arm 8_0

hartmann6: 0.017 [-0.175, 0.210]
l2norm: 1.451 [1.285, 1.618]

Parameterization:
x1: 0.43834762647747993
x2: 0.01964978128671646
x3: 0.22502082213759422
x4: 0.7010497134178877
x5: 0.8200943367555737
x6: 0.7476914403960109", "Arm 9_0

hartmann6: -0.069 [-0.261, 0.124]
l2norm: 1.288 [1.117, 1.458]

Parameterization:
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x2: 0.04954400472342968
x3: 0.3118802411481738
x4: 0.5614874539896846
x5: 0.6237162770703435
x6: 0.9516805456951261", "Arm 10_0

hartmann6: -0.23 [-0.423, -0.038]
l2norm: 1.254 [1.088, 1.421]

Parameterization:
x1: 0.013928516767919064
x2: 0.8675733413547277
x3: 0.5248574297875166
x4: 0.6198204094544053
x5: 0.3521989854052663
x6: 0.35793409403413534", "Arm 11_0

hartmann6: -0.034 [-0.227, 0.159]
l2norm: 1.6 [1.427, 1.773]

Parameterization:
x1: 0.10638012737035751
x2: 0.9256733832880855
x3: 0.3471939144656062
x4: 0.7353604743257165
x5: 0.14430653676390648
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hartmann6: -1.127 [-1.308, -0.946]
l2norm: 1.213 [1.080, 1.346]

Parameterization:
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x2: 0.6866303111729859
x3: 0.6161594597767127
x4: 0.5959654157152262
x5: 0.3959626615886123
x6: 0.23565533436845468", "Arm 13_0

hartmann6: -0.773 [-0.958, -0.588]
l2norm: 1.106 [0.974, 1.237]

Parameterization:
x1: 0.2114001689955874
x2: 0.6598251673457936
x3: 0.629483578828031
x4: 0.5768654723129062
x5: 0.2562493443252856
x6: 0.22657214115599586", "Arm 14_0

hartmann6: -1.906 [-2.052, -1.761]
l2norm: 1.223 [1.134, 1.312]

Parameterization:
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x2: 0.6902736821080439
x3: 0.614336939034702
x4: 0.612204582470053
x5: 0.3338366081900223
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hartmann6: -1.669 [-1.846, -1.492]
l2norm: 1.174 [1.051, 1.298]

Parameterization:
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x2: 0.6578164344992266
x3: 0.6118187105656752
x4: 0.6030546811245218
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hartmann6: -2.227 [-2.363, -2.092]
l2norm: 1.286 [1.189, 1.383]

Parameterization:
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x3: 0.6192184099313921
x4: 0.6361527822996007
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hartmann6: -2.279 [-2.447, -2.111]
l2norm: 1.332 [1.210, 1.453]

Parameterization:
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x3: 0.5506345147574029
x4: 0.6326688218781511
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hartmann6: -2.158 [-2.324, -1.992]
l2norm: 1.275 [1.156, 1.393]

Parameterization:
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hartmann6: -0.295 [-0.491, -0.099]
l2norm: 1.541 [1.345, 1.737]

Parameterization:
x1: 0.5094669461250305
x2: 0.028961949050426483
x3: 0.9195249676704407
x4: 0.7185776829719543
x5: 0.20534470677375793
x6: 0.7453696727752686", "Arm 1_0

hartmann6: -0.335 [-0.531, -0.139]
l2norm: 1.784 [1.588, 1.980]

Parameterization:
x1: 0.030807215720415115
x2: 0.7333147255703807
x3: 0.8054188275709748
x4: 0.7325294045731425
x5: 0.22661086171865463
x6: 0.9958701143041253", "Arm 2_0

hartmann6: 0.07 [-0.126, 0.266]
l2norm: 1.535 [1.339, 1.731]

Parameterization:
x1: 0.5449186321347952
x2: 0.9504998587071896
x3: 0.9345201617106795
x4: 0.003054482862353325
x5: 0.6934341117739677
x6: 0.049952831119298935", "Arm 3_0

hartmann6: -0.205 [-0.401, -0.009]
l2norm: 1.506 [1.310, 1.702]

Parameterization:
x1: 0.4581432929262519
x2: 0.8628739174455404
x3: 0.585976418107748
x4: 0.04202813468873501
x5: 0.9284532889723778
x6: 0.16748409066349268", "Arm 4_0

hartmann6: -0.101 [-0.297, 0.095]
l2norm: 1.122 [0.926, 1.318]

Parameterization:
x1: 0.8549876464530826
x2: 0.11792286671698093
x3: 0.4178288094699383
x4: 0.5888091530650854
x5: 0.23549478594213724
x6: 0.005349679850041866", "Arm 5_0

hartmann6: -0.09 [-0.286, 0.106]
l2norm: 1.013 [0.817, 1.209]

Parameterization:
x1: 0.060659466311335564
x2: 0.36236009281128645
x3: 0.6985868457704782
x4: 0.5339070362970233
x5: 0.16258792020380497
x6: 0.22701952792704105", "Arm 6_0

hartmann6: -0.015 [-0.211, 0.181]
l2norm: 1.499 [1.303, 1.695]

Parameterization:
x1: 0.6819224553182721
x2: 0.0455122971907258
x3: 0.27645703963935375
x4: 0.682553194463253
x5: 0.8880256414413452
x6: 0.9263124475255609", "Arm 7_0

hartmann6: -0.55 [-0.746, -0.354]
l2norm: 1.615 [1.419, 1.811]

Parameterization:
x1: 0.6430023284628987
x2: 0.8068088106811047
x3: 0.6025278307497501
x4: 0.5421762457117438
x5: 0.8732241541147232
x6: 0.26390309911221266", "Arm 8_0

hartmann6: 0.023 [-0.173, 0.219]
l2norm: 1.468 [1.272, 1.664]

Parameterization:
x1: 0.43834762647747993
x2: 0.01964978128671646
x3: 0.22502082213759422
x4: 0.7010497134178877
x5: 0.8200943367555737
x6: 0.7476914403960109", "Arm 9_0

hartmann6: -0.066 [-0.262, 0.130]
l2norm: 1.227 [1.031, 1.423]

Parameterization:
x1: 0.33409237023442984
x2: 0.04954400472342968
x3: 0.3118802411481738
x4: 0.5614874539896846
x5: 0.6237162770703435
x6: 0.9516805456951261", "Arm 10_0

hartmann6: -0.227 [-0.423, -0.031]
l2norm: 1.236 [1.040, 1.432]

Parameterization:
x1: 0.013928516767919064
x2: 0.8675733413547277
x3: 0.5248574297875166
x4: 0.6198204094544053
x5: 0.3521989854052663
x6: 0.35793409403413534", "Arm 11_0

hartmann6: -0.026 [-0.222, 0.170]
l2norm: 1.622 [1.426, 1.818]

Parameterization:
x1: 0.10638012737035751
x2: 0.9256733832880855
x3: 0.3471939144656062
x4: 0.7353604743257165
x5: 0.14430653676390648
x6: 0.8858285704627633", "Arm 12_0

hartmann6: -1.094 [-1.290, -0.898]
l2norm: 1.21 [1.014, 1.406]

Parameterization:
x1: 0.28955512219069973
x2: 0.6866303111729859
x3: 0.6161594597767127
x4: 0.5959654157152262
x5: 0.3959626615886123
x6: 0.23565533436845468", "Arm 13_0

hartmann6: -0.772 [-0.968, -0.576]
l2norm: 1.093 [0.897, 1.289]

Parameterization:
x1: 0.2114001689955874
x2: 0.6598251673457936
x3: 0.629483578828031
x4: 0.5768654723129062
x5: 0.2562493443252856
x6: 0.22657214115599586", "Arm 14_0

hartmann6: -1.959 [-2.155, -1.763]
l2norm: 1.137 [0.941, 1.333]

Parameterization:
x1: 0.3835770872100636
x2: 0.6902736821080439
x3: 0.614336939034702
x4: 0.612204582470053
x5: 0.3338366081900223
x6: 0.16930900485726838", "Arm 15_0

hartmann6: -1.631 [-1.827, -1.435]
l2norm: 1.142 [0.946, 1.338]

Parameterization:
x1: 0.4113735568794019
x2: 0.6578164344992266
x3: 0.6118187105656752
x4: 0.6030546811245218
x5: 0.24509284301974327
x6: 0.16378593941080893", "Arm 16_0

hartmann6: -2.245 [-2.441, -2.049]
l2norm: 1.219 [1.023, 1.415]

Parameterization:
x1: 0.4011566789789615
x2: 0.7288091274911536
x3: 0.6192184099313921
x4: 0.6361527822996007
x5: 0.3388579795862753
x6: 0.11856189457534973", "Arm 17_0

hartmann6: -2.314 [-2.510, -2.118]
l2norm: 1.464 [1.268, 1.660]

Parameterization:
x1: 0.43351642045594785
x2: 0.7342402117013916
x3: 0.5506345147574029
x4: 0.6326688218781511
x5: 0.36363810803812213
x6: 0.11214964609541407", "Arm 18_0

hartmann6: -2.172 [-2.368, -1.976]
l2norm: 1.329 [1.133, 1.525]

Parameterization:
x1: 0.422282102757064
x2: 0.6971691688844808
x3: 0.6887101325469829
x4: 0.6235261603801038
x5: 0.3305488294966215
x6: 0.10830150156449667" ], [ "Arm 0_0

hartmann6: -0.294 [-0.487, -0.100]
l2norm: 1.516 [1.341, 1.691]

Parameterization:
x1: 0.5094669461250305
x2: 0.028961949050426483
x3: 0.9195249676704407
x4: 0.7185776829719543
x5: 0.20534470677375793
x6: 0.7453696727752686", "Arm 1_0

hartmann6: -0.331 [-0.523, -0.138]
l2norm: 1.719 [1.546, 1.892]

Parameterization:
x1: 0.030807215720415115
x2: 0.7333147255703807
x3: 0.8054188275709748
x4: 0.7325294045731425
x5: 0.22661086171865463
x6: 0.9958701143041253", "Arm 2_0

hartmann6: 0.058 [-0.135, 0.250]
l2norm: 1.517 [1.344, 1.690]

Parameterization:
x1: 0.5449186321347952
x2: 0.9504998587071896
x3: 0.9345201617106795
x4: 0.003054482862353325
x5: 0.6934341117739677
x6: 0.049952831119298935", "Arm 3_0

hartmann6: -0.204 [-0.397, -0.011]
l2norm: 1.504 [1.331, 1.676]

Parameterization:
x1: 0.4581432929262519
x2: 0.8628739174455404
x3: 0.585976418107748
x4: 0.04202813468873501
x5: 0.9284532889723778
x6: 0.16748409066349268", "Arm 4_0

hartmann6: -0.11 [-0.303, 0.084]
l2norm: 1.179 [1.004, 1.354]

Parameterization:
x1: 0.8549876464530826
x2: 0.11792286671698093
x3: 0.4178288094699383
x4: 0.5888091530650854
x5: 0.23549478594213724
x6: 0.005349679850041866", "Arm 5_0

hartmann6: -0.098 [-0.291, 0.094]
l2norm: 1.072 [0.904, 1.240]

Parameterization:
x1: 0.060659466311335564
x2: 0.36236009281128645
x3: 0.6985868457704782
x4: 0.5339070362970233
x5: 0.16258792020380497
x6: 0.22701952792704105", "Arm 6_0

hartmann6: -0.019 [-0.212, 0.173]
l2norm: 1.475 [1.308, 1.643]

Parameterization:
x1: 0.6819224553182721
x2: 0.0455122971907258
x3: 0.27645703963935375
x4: 0.682553194463253
x5: 0.8880256414413452
x6: 0.9263124475255609", "Arm 7_0

hartmann6: -0.55 [-0.743, -0.357]
l2norm: 1.579 [1.406, 1.753]

Parameterization:
x1: 0.6430023284628987
x2: 0.8068088106811047
x3: 0.6025278307497501
x4: 0.5421762457117438
x5: 0.8732241541147232
x6: 0.26390309911221266", "Arm 8_0

hartmann6: 0.017 [-0.175, 0.210]
l2norm: 1.451 [1.285, 1.618]

Parameterization:
x1: 0.43834762647747993
x2: 0.01964978128671646
x3: 0.22502082213759422
x4: 0.7010497134178877
x5: 0.8200943367555737
x6: 0.7476914403960109", "Arm 9_0

hartmann6: -0.069 [-0.261, 0.124]
l2norm: 1.288 [1.117, 1.458]

Parameterization:
x1: 0.33409237023442984
x2: 0.04954400472342968
x3: 0.3118802411481738
x4: 0.5614874539896846
x5: 0.6237162770703435
x6: 0.9516805456951261", "Arm 10_0

hartmann6: -0.23 [-0.423, -0.038]
l2norm: 1.254 [1.088, 1.421]

Parameterization:
x1: 0.013928516767919064
x2: 0.8675733413547277
x3: 0.5248574297875166
x4: 0.6198204094544053
x5: 0.3521989854052663
x6: 0.35793409403413534", "Arm 11_0

hartmann6: -0.034 [-0.227, 0.159]
l2norm: 1.6 [1.427, 1.773]

Parameterization:
x1: 0.10638012737035751
x2: 0.9256733832880855
x3: 0.3471939144656062
x4: 0.7353604743257165
x5: 0.14430653676390648
x6: 0.8858285704627633", "Arm 12_0

hartmann6: -1.127 [-1.308, -0.946]
l2norm: 1.213 [1.080, 1.346]

Parameterization:
x1: 0.28955512219069973
x2: 0.6866303111729859
x3: 0.6161594597767127
x4: 0.5959654157152262
x5: 0.3959626615886123
x6: 0.23565533436845468", "Arm 13_0

hartmann6: -0.773 [-0.958, -0.588]
l2norm: 1.106 [0.974, 1.237]

Parameterization:
x1: 0.2114001689955874
x2: 0.6598251673457936
x3: 0.629483578828031
x4: 0.5768654723129062
x5: 0.2562493443252856
x6: 0.22657214115599586", "Arm 14_0

hartmann6: -1.906 [-2.052, -1.761]
l2norm: 1.223 [1.134, 1.312]

Parameterization:
x1: 0.3835770872100636
x2: 0.6902736821080439
x3: 0.614336939034702
x4: 0.612204582470053
x5: 0.3338366081900223
x6: 0.16930900485726838", "Arm 15_0

hartmann6: -1.669 [-1.846, -1.492]
l2norm: 1.174 [1.051, 1.298]

Parameterization:
x1: 0.4113735568794019
x2: 0.6578164344992266
x3: 0.6118187105656752
x4: 0.6030546811245218
x5: 0.24509284301974327
x6: 0.16378593941080893", "Arm 16_0

hartmann6: -2.227 [-2.363, -2.092]
l2norm: 1.286 [1.189, 1.383]

Parameterization:
x1: 0.4011566789789615
x2: 0.7288091274911536
x3: 0.6192184099313921
x4: 0.6361527822996007
x5: 0.3388579795862753
x6: 0.11856189457534973", "Arm 17_0

hartmann6: -2.279 [-2.447, -2.111]
l2norm: 1.332 [1.210, 1.453]

Parameterization:
x1: 0.43351642045594785
x2: 0.7342402117013916
x3: 0.5506345147574029
x4: 0.6326688218781511
x5: 0.36363810803812213
x6: 0.11214964609541407", "Arm 18_0

hartmann6: -2.158 [-2.324, -1.992]
l2norm: 1.275 [1.156, 1.393]

Parameterization:
x1: 0.422282102757064
x2: 0.6971691688844808
x3: 0.6887101325469829
x4: 0.6235261603801038
x5: 0.3305488294966215
x6: 0.10830150156449667" ] ], "y": [ [ 1.540891301510101, 1.784087313450029, 1.534787228368841, 1.5056426174057556, 1.1224233900647862, 1.0130303221267658, 1.499250878657248, 1.6147618494568816, 1.4675495105439027, 1.2267603401526384, 1.2361587110258938, 1.6224940867238529, 1.2104556932471395, 1.0928373677503216, 1.1370471525753243, 1.141971020576065, 1.219327749244669, 1.4635667930128662, 1.3291978604406216 ], [ 1.5160658387101562, 1.7187970415693692, 1.5174047788237188, 1.5036039033674609, 1.1787460029388532, 1.0721227758983927, 1.4754054370979546, 1.5793498543732187, 1.4511385258796823, 1.2877404035715168, 1.2544102348546462, 1.599861028351692, 1.212713358051166, 1.1055232907321193, 1.2230543158348905, 1.1742830241716458, 1.2858331544107595, 1.331684153662896, 1.2745046154516773 ] ] }, { "yaxis.title": "l2norm" } ], "label": "l2norm", "method": "update" } ], "x": 1.25, "xanchor": "left", "y": 0.72, "yanchor": "middle" } ], "width": 900, "xaxis": { "title": { "text": "hartmann6" }, "zeroline": true, "zerolinecolor": "red" }, "yaxis": { "title": { "text": "l2norm" }, "zeroline": true, "zerolinecolor": "red" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "render(plot_objective_vs_constraints(model, 'hartmann6', rel=False))" ] }, { "cell_type": "markdown", "metadata": { "originalKey": "f2d4fae3-2140-45d0-8142-49b91548ca59" }, "source": [ "## 4. Cross-validation plots\n", "\n", "CV plots are useful to check how well the model predictions calibrate against the actual measurements. If all points are close to the dashed line, then the model is a good predictor of the real data." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2022-12-29T21:31:05.679808Z", "iopub.status.busy": "2022-12-29T21:31:05.679114Z", "iopub.status.idle": "2022-12-29T21:31:05.918387Z", "shell.execute_reply": "2022-12-29T21:31:05.917835Z" }, "executionStartTime": 1627397871181, "executionStopTime": 1627397871526, "originalKey": "f770f8a9-466c-4fd2-b268-3a0d166482f3", "requestMsgId": "d6242810-a316-4e2b-b9dd-dd4c56b725b7" }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "hoverinfo": "none", "line": { "color": "black", "dash": "dot", "width": 2 }, "mode": "lines", "showlegend": false, "type": "scatter", "visible": true, "x": [ 0.7588774725606027, 2.038240163016192 ], "y": [ 0.7588774725606027, 2.038240163016192 ] }, { "error_x": { "array": [ 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "error_y": { "array": [ 0.3914853760237202, 0.3702486631384058, 0.36784612326184407, 0.35978946454672833, 0.3871859507367257, 0.323990447603746, 0.3220042581462568, 0.37535396420681355, 0.3149997522171872, 0.346118230592325, 0.31649451937711803, 0.3704925525389591, 0.181353363518817, 0.1764997029324853, 0.10012369689967067, 0.15931036612488222, 0.11127150246119188, 0.1551798053718403, 0.14786841139075677 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "hoverinfo": "text", "marker": { "color": "rgba(128,177,211,1)" }, "mode": "markers", "name": "In-sample", "showlegend": true, "text": [ "Arm 0_0

Actual Outcome: 1.541 [1.345, 1.737]
Predicted Outcome: 1.417 [1.026, 1.809]

Parameterization:
x1: 0.5094669461250305
x2: 0.028961949050426483
x3: 0.9195249676704407
x4: 0.7185776829719543
x5: 0.20534470677375793
x6: 0.7453696727752686", "Arm 1_0

Actual Outcome: 1.784 [1.588, 1.980]
Predicted Outcome: 1.486 [1.116, 1.856]

Parameterization:
x1: 0.030807215720415115
x2: 0.7333147255703807
x3: 0.8054188275709748
x4: 0.7325294045731425
x5: 0.22661086171865463
x6: 0.9958701143041253", "Arm 2_0

Actual Outcome: 1.535 [1.339, 1.731]
Predicted Outcome: 1.456 [1.088, 1.824]

Parameterization:
x1: 0.5449186321347952
x2: 0.9504998587071896
x3: 0.9345201617106795
x4: 0.003054482862353325
x5: 0.6934341117739677
x6: 0.049952831119298935", "Arm 3_0

Actual Outcome: 1.506 [1.310, 1.702]
Predicted Outcome: 1.497 [1.137, 1.857]

Parameterization:
x1: 0.4581432929262519
x2: 0.8628739174455404
x3: 0.585976418107748
x4: 0.04202813468873501
x5: 0.9284532889723778
x6: 0.16748409066349268", "Arm 4_0

Actual Outcome: 1.122 [0.926, 1.318]
Predicted Outcome: 1.399 [1.011, 1.786]

Parameterization:
x1: 0.8549876464530826
x2: 0.11792286671698093
x3: 0.4178288094699383
x4: 0.5888091530650854
x5: 0.23549478594213724
x6: 0.005349679850041866", "Arm 5_0

Actual Outcome: 1.013 [0.817, 1.209]
Predicted Outcome: 1.234 [0.910, 1.558]

Parameterization:
x1: 0.060659466311335564
x2: 0.36236009281128645
x3: 0.6985868457704782
x4: 0.5339070362970233
x5: 0.16258792020380497
x6: 0.22701952792704105", "Arm 6_0

Actual Outcome: 1.499 [1.303, 1.695]
Predicted Outcome: 1.411 [1.089, 1.733]

Parameterization:
x1: 0.6819224553182721
x2: 0.0455122971907258
x3: 0.27645703963935375
x4: 0.682553194463253
x5: 0.8880256414413452
x6: 0.9263124475255609", "Arm 7_0

Actual Outcome: 1.615 [1.419, 1.811]
Predicted Outcome: 1.449 [1.074, 1.825]

Parameterization:
x1: 0.6430023284628987
x2: 0.8068088106811047
x3: 0.6025278307497501
x4: 0.5421762457117438
x5: 0.8732241541147232
x6: 0.26390309911221266", "Arm 8_0

Actual Outcome: 1.468 [1.272, 1.664]
Predicted Outcome: 1.409 [1.094, 1.724]

Parameterization:
x1: 0.43834762647747993
x2: 0.01964978128671646
x3: 0.22502082213759422
x4: 0.7010497134178877
x5: 0.8200943367555737
x6: 0.7476914403960109", "Arm 9_0

Actual Outcome: 1.227 [1.031, 1.423]
Predicted Outcome: 1.478 [1.132, 1.824]

Parameterization:
x1: 0.33409237023442984
x2: 0.04954400472342968
x3: 0.3118802411481738
x4: 0.5614874539896846
x5: 0.6237162770703435
x6: 0.9516805456951261", "Arm 10_0

Actual Outcome: 1.236 [1.040, 1.432]
Predicted Outcome: 1.302 [0.986, 1.618]

Parameterization:
x1: 0.013928516767919064
x2: 0.8675733413547277
x3: 0.5248574297875166
x4: 0.6198204094544053
x5: 0.3521989854052663
x6: 0.35793409403413534", "Arm 11_0

Actual Outcome: 1.622 [1.426, 1.818]
Predicted Outcome: 1.519 [1.148, 1.889]

Parameterization:
x1: 0.10638012737035751
x2: 0.9256733832880855
x3: 0.3471939144656062
x4: 0.7353604743257165
x5: 0.14430653676390648
x6: 0.8858285704627633", "Arm 12_0

Actual Outcome: 1.21 [1.014, 1.406]
Predicted Outcome: 1.215 [1.033, 1.396]

Parameterization:
x1: 0.28955512219069973
x2: 0.6866303111729859
x3: 0.6161594597767127
x4: 0.5959654157152262
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x6: 0.23565533436845468", "Arm 13_0

Actual Outcome: 1.093 [0.897, 1.289]
Predicted Outcome: 1.116 [0.939, 1.292]

Parameterization:
x1: 0.2114001689955874
x2: 0.6598251673457936
x3: 0.629483578828031
x4: 0.5768654723129062
x5: 0.2562493443252856
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Actual Outcome: 1.137 [0.941, 1.333]
Predicted Outcome: 1.245 [1.145, 1.346]

Parameterization:
x1: 0.3835770872100636
x2: 0.6902736821080439
x3: 0.614336939034702
x4: 0.612204582470053
x5: 0.3338366081900223
x6: 0.16930900485726838", "Arm 15_0

Actual Outcome: 1.142 [0.946, 1.338]
Predicted Outcome: 1.196 [1.036, 1.355]

Parameterization:
x1: 0.4113735568794019
x2: 0.6578164344992266
x3: 0.6118187105656752
x4: 0.6030546811245218
x5: 0.24509284301974327
x6: 0.16378593941080893", "Arm 16_0

Actual Outcome: 1.219 [1.023, 1.415]
Predicted Outcome: 1.307 [1.196, 1.419]

Parameterization:
x1: 0.4011566789789615
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x3: 0.6192184099313921
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Actual Outcome: 1.464 [1.268, 1.660]
Predicted Outcome: 1.249 [1.094, 1.404]

Parameterization:
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x3: 0.5506345147574029
x4: 0.6326688218781511
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x6: 0.11214964609541407", "Arm 18_0

Actual Outcome: 1.329 [1.133, 1.525]
Predicted Outcome: 1.243 [1.096, 1.391]

Parameterization:
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Actual Outcome: -0.295 [-0.491, -0.099]
Predicted Outcome: -0.248 [-1.412, 0.915]

Parameterization:
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Actual Outcome: -0.335 [-0.531, -0.139]
Predicted Outcome: -0.182 [-1.263, 0.898]

Parameterization:
x1: 0.030807215720415115
x2: 0.7333147255703807
x3: 0.8054188275709748
x4: 0.7325294045731425
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Actual Outcome: 0.07 [-0.126, 0.266]
Predicted Outcome: -0.316 [-1.386, 0.754]

Parameterization:
x1: 0.5449186321347952
x2: 0.9504998587071896
x3: 0.9345201617106795
x4: 0.003054482862353325
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Actual Outcome: -0.205 [-0.401, -0.009]
Predicted Outcome: -0.176 [-1.237, 0.886]

Parameterization:
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Actual Outcome: -0.101 [-0.297, 0.095]
Predicted Outcome: -0.403 [-1.571, 0.764]

Parameterization:
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Actual Outcome: -0.09 [-0.286, 0.106]
Predicted Outcome: -0.326 [-1.349, 0.697]

Parameterization:
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Actual Outcome: -0.015 [-0.211, 0.181]
Predicted Outcome: -0.141 [-1.186, 0.903]

Parameterization:
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x3: 0.27645703963935375
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Actual Outcome: -0.55 [-0.746, -0.354]
Predicted Outcome: -0.553 [-1.688, 0.582]

Parameterization:
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x3: 0.6025278307497501
x4: 0.5421762457117438
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Actual Outcome: 0.023 [-0.173, 0.219]
Predicted Outcome: -0.135 [-1.149, 0.879]

Parameterization:
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x3: 0.22502082213759422
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Actual Outcome: -0.066 [-0.262, 0.130]
Predicted Outcome: -0.152 [-1.220, 0.917]

Parameterization:
x1: 0.33409237023442984
x2: 0.04954400472342968
x3: 0.3118802411481738
x4: 0.5614874539896846
x5: 0.6237162770703435
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Actual Outcome: -0.227 [-0.423, -0.031]
Predicted Outcome: -0.327 [-1.353, 0.699]

Parameterization:
x1: 0.013928516767919064
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x3: 0.5248574297875166
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Actual Outcome: -0.026 [-0.222, 0.170]
Predicted Outcome: -0.298 [-1.378, 0.782]

Parameterization:
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x2: 0.9256733832880855
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Actual Outcome: -1.094 [-1.290, -0.898]
Predicted Outcome: -1.319 [-1.791, -0.848]

Parameterization:
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Actual Outcome: -0.772 [-0.968, -0.576]
Predicted Outcome: -0.781 [-1.338, -0.225]

Parameterization:
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Actual Outcome: -1.959 [-2.155, -1.763]
Predicted Outcome: -1.843 [-2.059, -1.626]

Parameterization:
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Actual Outcome: -1.631 [-1.827, -1.435]
Predicted Outcome: -1.836 [-2.248, -1.425]

Parameterization:
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Actual Outcome: -2.245 [-2.441, -2.049]
Predicted Outcome: -2.211 [-2.399, -2.022]

Parameterization:
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Actual Outcome: -2.314 [-2.510, -2.118]
Predicted Outcome: -2.183 [-2.508, -1.858]

Parameterization:
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Actual Outcome: -2.172 [-2.368, -1.976]
Predicted Outcome: -2.122 [-2.436, -1.809]

Parameterization:
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cv_results = cross_validate(model)\n", "render(interact_cross_validation(cv_results))" ] }, { "cell_type": "markdown", "metadata": { "originalKey": "40f8ee99-fee8-4fd9-9cff-a7aa230dd5ae" }, "source": [ "## 5. Slice plots\n", "\n", "Slice plots show the metric outcome as a function of one parameter while fixing the others. 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Parameterization:
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hartmann6: -0.23 [-0.423, -0.038]

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Parameterization:
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Parameterization:
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Parameterization:
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