{ "cells": [ { "cell_type": "markdown", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "95e7a97a-bf78-48d4-a0c1-c0e8dfc4fed9", "showInput": true }, "source": [ "# Multi-Objective Optimization Ax API\n", "### Using the Service API\n", "For Multi-objective optimization (MOO) in the `AxClient`, objectives are specified through the `ObjectiveProperties` dataclass. An `ObjectiveProperties` requires a boolean `minimize`, and also accepts an optional floating point `threshold`. If a `threshold` is not specified, Ax will infer it through the use of heuristics. If the user knows the region of interest (because they have specs or prior knowledge), then specifying the thresholds is preferable to inferring it. But if the user would need to guess, inferring is preferable.\n", "\n", "\n", "To learn more about how to choose a threshold, see [Set Objective Thresholds to focus candidate generation in a region of interest](#Set-Objective-Thresholds-to-focus-candidate-generation-in-a-region-of-interest). See the [Service API Tutorial](/tutorials/gpei_hartmann_service.html) for more infomation on running experiments with the Service API." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "code_folding": [], "customInput": null, "execution": { "iopub.execute_input": "2023-08-11T16:07:54.580652Z", "iopub.status.busy": "2023-08-11T16:07:54.580060Z", "iopub.status.idle": "2023-08-11T16:08:02.742560Z", "shell.execute_reply": "2023-08-11T16:08:02.741133Z" }, "hidden_ranges": [], "originalKey": "06bf2029-0ea4-40b4-aced-956f1411cb6e", "showInput": true }, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] 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": [ "from ax.service.ax_client import AxClient\n", "from ax.service.utils.instantiation import ObjectiveProperties\n", "\n", "import torch\n", "\n", "# Plotting imports and initialization\n", "from ax.utils.notebook.plotting import render, init_notebook_plotting\n", "from ax.plot.pareto_utils import compute_posterior_pareto_frontier\n", "from ax.plot.pareto_frontier import plot_pareto_frontier\n", "\n", "init_notebook_plotting()\n", "\n", "# Load our sample 2-objective problem\n", "from botorch.test_functions.multi_objective import BraninCurrin\n", "\n", "branin_currin = BraninCurrin(negate=True).to(\n", " dtype=torch.double,\n", " device=torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\"),\n", ")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "code_folding": [], "customInput": null, "execution": { "iopub.execute_input": "2023-08-11T16:08:02.774452Z", "iopub.status.busy": "2023-08-11T16:08:02.774114Z", "iopub.status.idle": "2023-08-11T16:08:02.783872Z", "shell.execute_reply": "2023-08-11T16:08:02.783366Z" }, "executionStartTime": 1628191188673, "executionStopTime": 1628191188746, "hidden_ranges": [], "originalKey": "c687973d-1b09-4a8f-9108-1f74adf64d4d", "requestMsgId": "ea523260-8896-48e4-a62f-3530d268b209", "showInput": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] 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 08-11 12:08:02] 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 08-11 12:08:02] 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 08-11 12:08:02] 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])], parameter_constraints=[]).\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.core.experiment: The is_test flag has been set to True. This flag is meant purely for development and integration testing purposes. If you are running a live experiment, please set this flag to False\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.modelbridge.dispatch_utils: Using Models.MOO since there are more ordered parameters than there are categories for the unordered categorical parameters.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.modelbridge.dispatch_utils: Calculating the number of remaining initialization trials based on num_initialization_trials=None max_initialization_trials=None num_tunable_parameters=2 num_trials=None use_batch_trials=False\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=5\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=5\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+MOO', steps=[Sobol for 5 trials, MOO for subsequent trials]). Iterations after 5 will take longer to generate due to model-fitting.\n" ] } ], "source": [ "ax_client = AxClient()\n", "ax_client.create_experiment(\n", " name=\"moo_experiment\",\n", " parameters=[\n", " {\n", " \"name\": f\"x{i+1}\",\n", " \"type\": \"range\",\n", " \"bounds\": [0.0, 1.0],\n", " }\n", " for i in range(2)\n", " ],\n", " objectives={\n", " # `threshold` arguments are optional\n", " \"a\": ObjectiveProperties(minimize=False, threshold=branin_currin.ref_point[0]),\n", " \"b\": ObjectiveProperties(minimize=False, threshold=branin_currin.ref_point[1]),\n", " },\n", " overwrite_existing_experiment=True,\n", " is_test=True,\n", ")" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "70fd45e1-a2ce-4034-bb44-086507833472", "showInput": true }, "source": [ "### Create an Evaluation Function\n", "In the case of MOO experiments, evaluation functions can be any arbitrary function that takes in a `dict` of parameter names mapped to values and returns a `dict` of objective names mapped to a `tuple` of mean and SEM values." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "code_folding": [], "customInput": null, "execution": { "iopub.execute_input": "2023-08-11T16:08:02.787198Z", "iopub.status.busy": "2023-08-11T16:08:02.787018Z", "iopub.status.idle": "2023-08-11T16:08:02.790091Z", "shell.execute_reply": "2023-08-11T16:08:02.789604Z" }, "executionStartTime": 1628191201840, "executionStopTime": 1628191201871, "hidden_ranges": [], "originalKey": "a0e4fa8d-ebc7-4dc6-b370-ed4a83e3208f", "requestMsgId": "9cfd336d-c317-4d1c-a028-42d45903bac6", "showInput": true }, "outputs": [], "source": [ "def evaluate(parameters):\n", " evaluation = branin_currin(\n", " torch.tensor([parameters.get(\"x1\"), parameters.get(\"x2\")])\n", " )\n", " # In our case, standard error is 0, since we are computing a synthetic function.\n", " # Set standard error to None if the noise level is unknown.\n", " return {\"a\": (evaluation[0].item(), 0.0), \"b\": (evaluation[1].item(), 0.0)}" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "4200cd7c-8e13-4cbf-b0c1-72b52d900aaf", "showInput": true }, "source": [ "### Run Optimization" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "customInput": null, "execution": { "iopub.execute_input": "2023-08-11T16:08:02.792602Z", "iopub.status.busy": "2023-08-11T16:08:02.792400Z", "iopub.status.idle": "2023-08-11T16:08:18.928394Z", "shell.execute_reply": "2023-08-11T16:08:18.927622Z" }, "executionStartTime": 1628191208271, "executionStopTime": 1628191238749, "originalKey": "f91b1a1e-c78a-4262-a211-a13115c007c1", "requestMsgId": "842a1cf8-97a3-43d6-83a3-f258ea96ae20", "showInput": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.701518, 'x2': 0.156306}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.service.ax_client: Completed trial 0 with data: {'a': (-18.383011, 0.0), 'b': (-10.296076, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.929243, 'x2': 0.589945}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.service.ax_client: Completed trial 1 with data: {'a': (-47.122696, 0.0), 'b': (-5.857306, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.445229, 'x2': 0.810535}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.service.ax_client: Completed trial 2 with data: {'a': (-80.631577, 0.0), 'b': (-5.575551, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.796297, 'x2': 0.309085}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.service.ax_client: Completed trial 3 with data: {'a': (-29.540968, 0.0), 'b': (-8.395409, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.20532, 'x2': 0.864158}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:02] ax.service.ax_client: Completed trial 4 with data: {'a': (-18.477371, 0.0), 'b': (-6.056166, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:03] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.032248, 'x2': 0.630939}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:03] ax.service.ax_client: Completed trial 5 with data: {'a': (-48.562492, 0.0), 'b': (-3.432099, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:04] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.206069, 'x2': 0.612144}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:04] ax.service.ax_client: Completed trial 6 with data: {'a': (-6.92124, 0.0), 'b': (-7.695414, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:04] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.150912, 'x2': 0.030117}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:04] ax.service.ax_client: Completed trial 7 with data: {'a': (-119.343346, 0.0), 'b': (-13.202106, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:05] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.0, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:05] ax.service.ax_client: Completed trial 8 with data: {'a': (-17.508297, 0.0), 'b': (-1.180408, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:05] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.067296, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:05] ax.service.ax_client: Completed trial 9 with data: {'a': (-4.005313, 0.0), 'b': (-3.663518, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:06] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.031327, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:06] ax.service.ax_client: Completed trial 10 with data: {'a': (-9.000585, 0.0), 'b': (-2.4325, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:07] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.060198, 'x2': 0.908685}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:07] ax.service.ax_client: Completed trial 11 with data: {'a': (-5.578178, 0.0), 'b': (-3.706179, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:07] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.014968, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:07] ax.service.ax_client: Completed trial 12 with data: {'a': (-12.997011, 0.0), 'b': (-1.789565, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:08] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 1.0, 'x2': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:08] ax.service.ax_client: Completed trial 13 with data: {'a': (-10.960894, 0.0), 'b': (-10.179487, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:09] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 1.0, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:09] ax.service.ax_client: Completed trial 14 with data: {'a': (-145.872208, 0.0), 'b': (-4.005316, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:10] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.083267, 'x2': 0.954086}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:10] ax.service.ax_client: Completed trial 15 with data: {'a': (-2.400715, 0.0), 'b': (-4.251922, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:11] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.046384, 'x2': 0.990825}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:11] ax.service.ax_client: Completed trial 16 with data: {'a': (-6.334183, 0.0), 'b': (-3.005923, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:12] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.101107, 'x2': 0.896879}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:12] ax.service.ax_client: Completed trial 17 with data: {'a': (-1.070089, 0.0), 'b': (-4.892826, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:13] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.007324, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:13] ax.service.ax_client: Completed trial 18 with data: {'a': (-15.20262, 0.0), 'b': (-1.479727, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:14] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.022841, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:14] ax.service.ax_client: Completed trial 19 with data: {'a': (-10.947443, 0.0), 'b': (-2.103345, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:15] ax.service.ax_client: Generated new trial 20 with parameters {'x1': 0.055549, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:15] ax.service.ax_client: Completed trial 20 with data: {'a': (-5.032709, 0.0), 'b': (-3.296027, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:15] ax.service.ax_client: Generated new trial 21 with parameters {'x1': 0.731099, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:15] ax.service.ax_client: Completed trial 21 with data: {'a': (-212.2547, 0.0), 'b': (-4.18715, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:16] ax.service.ax_client: Generated new trial 22 with parameters {'x1': 0.038773, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:16] ax.service.ax_client: Completed trial 22 with data: {'a': (-7.524571, 0.0), 'b': (-2.711313, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:17] ax.service.ax_client: Generated new trial 23 with parameters {'x1': 0.073087, 'x2': 0.96351}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:17] ax.service.ax_client: Completed trial 23 with data: {'a': (-3.127445, 0.0), 'b': (-3.941511, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:18] ax.service.ax_client: Generated new trial 24 with parameters {'x1': 0.089731, 'x2': 0.919321}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-11 12:08:18] ax.service.ax_client: Completed trial 24 with data: {'a': (-1.693456, 0.0), 'b': (-4.539983, 0.0)}.\n" ] } ], "source": [ "for i in range(25):\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=evaluate(parameters))" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "e0a6feb4-8c38-42e4-9d7c-62b79307e043", "showInput": false }, "source": [ "### Plot Pareto Frontier" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "code_folding": [], "customInput": null, "execution": { "iopub.execute_input": "2023-08-11T16:08:18.931618Z", "iopub.status.busy": "2023-08-11T16:08:18.931368Z", "iopub.status.idle": "2023-08-11T16:08:35.530717Z", "shell.execute_reply": "2023-08-11T16:08:35.529997Z" }, "executionStartTime": 1628191262231, "executionStopTime": 1628191270720, "hidden_ranges": [], "originalKey": "c2c2b222-6b68-4f1a-839f-16b50019ada4", "requestMsgId": "563d345b-573c-4d93-a480-5db88a283250", "showInput": true }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "error_x": { "array": [ 0.07978367303976615, 0.06509189556743299, 0.055610241396747015, 0.07978367303976615, 0.06003821550065871, 0.05801771218443575, 0.05940509982900886, 0.054244326091660224, 0.07978367299821883, 0.05569519435897198, 0.06683168098792687, 0.055281247584075856, 0.05364103116639671, 0.053575108460539596, 0.05852082683614557, 0.056401654211125335, 0.06701153996669237, 0.05714897584221158, 0.05267343686656898, 0.07848021691883632 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "error_y": { "array": [ 0.004554850464694622, 0.003719995119627712, 0.0031606317857966926, 0.004554850464694622, 0.0034294215947934612, 0.0033119471520351006, 0.0033927317062300228, 0.0030885975853918446, 0.004554850474217118, 0.0031654622587426414, 0.003634407279747953, 0.0031489276564381267, 0.0030222621615233537, 0.003050112453551893, 0.0033413137246632984, 0.0032167587576818007, 0.0036793230149329294, 0.0031673051814150406, 0.0029866877111871014, 0.004178570311676646 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "hoverinfo": "text", "legendgroup": "mean", "marker": { "color": "rgba(128,177,211,1)" }, "mode": "markers", "name": "mean", "text": [ "Parameterization 0
a: -17.504 [-17.584, -17.424]
b: -1.18 [-1.185, -1.176]

Parameterization:
x1: 0.0
x2: 1.0", "Parameterization 1
a: -16.876 [-16.941, -16.811]
b: -1.26 [-1.264, -1.256]

Parameterization:
x1: 0.0019488612677646883
x2: 1.0", "Parameterization 2
a: -14.548 [-14.603, -14.492]
b: -1.57 [-1.573, -1.567]

Parameterization:
x1: 0.009532594052545147
x2: 1.0", "Parameterization 3
a: -17.504 [-17.584, -17.424]
b: -1.18 [-1.185, -1.176]

Parameterization:
x1: 0.0
x2: 1.0", "Parameterization 4
a: -16.521 [-16.581, -16.461]
b: -1.306 [-1.309, -1.303]

Parameterization:
x1: 0.0030681498403901802
x2: 1.0", "Parameterization 5
a: -16.311 [-16.369, -16.253]
b: -1.333 [-1.337, -1.330]

Parameterization:
x1: 0.0037346965838822863
x2: 1.0", "Parameterization 6
a: -16.462 [-16.521, -16.403]
b: -1.314 [-1.317, -1.310]

Parameterization:
x1: 0.0032545757263099245
x2: 1.0", "Parameterization 7
a: -11.909 [-11.963, -11.854]
b: -1.953 [-1.956, -1.950]

Parameterization:
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "objectives = ax_client.experiment.optimization_config.objective.objectives\n", "frontier = compute_posterior_pareto_frontier(\n", " experiment=ax_client.experiment,\n", " data=ax_client.experiment.fetch_data(),\n", " primary_objective=objectives[1].metric,\n", " secondary_objective=objectives[0].metric,\n", " absolute_metrics=[\"a\", \"b\"],\n", " num_points=20,\n", ")\n", "render(plot_pareto_frontier(frontier, CI_level=0.90))" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "f4f6ce29-4a0c-4ac5-84a7-f83a4de9112c", "showInput": true }, "source": [ "# Deep Dive\n", "\n", "In the rest of this tutorial, we will show two algorithms available in Ax for multi-objective optimization\n", "and visualize how they compare to eachother and to quasirandom search.\n", "\n", "MOO covers the case where we care about multiple\n", "outcomes in our experiment but we do not know before hand a specific weighting of those\n", "objectives (covered by `ScalarizedObjective`) or a specific constraint on one objective \n", "(covered by `OutcomeConstraint`s) that will produce the best result.\n", "\n", "The solution in this case is to find a whole Pareto frontier, a surface in outcome-space\n", "containing points that can't be improved on in every outcome. This shows us the\n", "tradeoffs between objectives that we can choose to make." ] }, { "cell_type": "markdown", "metadata": { "originalKey": "e04a24fa-dcfc-4430-960f-9c0e772fd754", "showInput": true }, "source": [ "### Problem Statement\n", "\n", "Optimize a list of M objective functions $ \\bigl(f^{(1)}( x),..., f^{(M)}( x) \\bigr)$ over a bounded search space $\\mathcal X \\subset \\mathbb R^d$.\n", "\n", "We assume $f^{(i)}$ are expensive-to-evaluate black-box functions with no known analytical expression, and no observed gradients. For instance, a machine learning model where we're interested in maximizing accuracy and minimizing inference time, with $\\mathcal X$ the set of possible configuration spaces" ] }, { "attachments": { "pareto_front%20%281%29.png": { "image/png": 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} }, "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "1842c5bf-4113-406b-b2c7-bc2535e9dd6c", "showInput": false }, "source": [ "### Pareto Optimality\n", "\n", "In a multi-objective optimization problem, there typically is no single best solution. Rather, the *goal* is to identify the set of Pareto optimal solutions such that any improvement in one objective means deteriorating another. Provided with the Pareto set, decision-makers can select an objective trade-off according to their preferences. In the plot below, the red dots are the Pareto optimal solutions (assuming both objectives are to be minimized).\n", "![pareto front](attachment:pareto_front%20%281%29.png)" ] }, { "attachments": { "hv_figure%20%281%29.png": { "image/png": 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} }, "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "cefa89be-ef41-40d9-9458-d6faed3c6c91", "showInput": false }, "source": [ "### Evaluating the Quality of a Pareto Front (Hypervolume)\n", "\n", "Given a reference point $ r \\in \\mathbb R^M$, which we represent as a list of M `ObjectiveThreshold`s, one for each coordinate, the hypervolume (HV) of a Pareto set $\\mathcal P = \\{ f(x_i)\\}_{i=1}^{|\\mathcal P|}$ is the volume of the space dominated (superior in every one of our M objectives) by $\\mathcal P$ and bounded from above by a point $ r$. The reference point should be set to be slightly worse (10% is reasonable) than the worst value of each objective that a decision maker would tolerate. In the figure below, the grey area is the hypervolume in this 2-objective problem.\n", "![hv_figure](attachment:hv_figure%20%281%29.png)" ] }, { "attachments": { "objective_thresholds_comparison.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "1819970e-9b48-4b57-b280-35bf2c4919d2", "showInput": false }, "source": [ "### Set Objective Thresholds to focus candidate generation in a region of interest\n", "\n", "The below plots show three different sets of points generated by the qNEHVI [1] algorithm with different objective thresholds (aka reference points). Note that here we use absolute thresholds, but thresholds can also be relative to a status_quo arm.\n", "\n", "The first plot shows the points without the `ObjectiveThreshold`s visible (they're set far below the origin of the graph).\n", "\n", "The second shows the points generated with (-18, -6) as thresholds. The regions violating the thresholds are greyed out. Only the white region in the upper right exceeds both threshold, points in this region dominate the intersection of these thresholds (this intersection is the reference point). Only points in this region contribute to the hypervolume objective. A few exploration points are not in the valid region, but almost all the rest of the points are.\n", "\n", "The third shows points generated with a very strict pair of thresholds, (-18, -2). Only the white region in the upper right exceeds both thresholds. Many points do not lie in the dominating region, but there are still more focused there than in the second examples.\n", "![objective_thresholds_comparison.png](attachment:objective_thresholds_comparison.png)" ] }, { "cell_type": "markdown", "metadata": { "originalKey": "f2f39a8f-279f-49a1-b645-d51caed24d9c" }, "source": [ "### Further Information\n", "A deeper explanation of our the qNEHVI [1] and qNParEGO [2] algorithms this notebook explores can be found at \n", "\n", "[1] [S. Daulton, M. Balandat, and E. Bakshy. Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement. Advances in Neural Information Processing Systems 34, 2021.](https://arxiv.org/abs/2105.08195)\n", "\n", "[2] [S. Daulton, M. Balandat, and E. Bakshy. Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization. Advances in Neural Information Processing Systems 33, 2020.](https://arxiv.org/abs/2006.05078)\n", "\n", "In addition, the underlying BoTorch implementation has a researcher-oriented tutorial at https://botorch.org/tutorials/multi_objective_bo." ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "0ac396dd-8040-4f87-8abe-472127734aef" }, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:35.534674Z", "iopub.status.busy": "2023-08-11T16:08:35.534392Z", "iopub.status.idle": "2023-08-11T16:08:35.538334Z", "shell.execute_reply": "2023-08-11T16:08:35.537778Z" }, "executionStartTime": 1628191302514, "executionStopTime": 1628191302546, "hidden_ranges": [], "originalKey": "500597fc-a996-48f4-a8fe-defd429162b8", "requestMsgId": "07dd11c9-cd20-4bfa-b2d9-9a7bf70b2e44" }, "outputs": [], "source": [ "import pandas as pd\n", "from ax import *\n", "\n", "import numpy as np\n", "\n", "from ax.core.metric import Metric\n", "from ax.metrics.noisy_function import NoisyFunctionMetric\n", "from ax.service.utils.report_utils import exp_to_df\n", "from ax.runners.synthetic import SyntheticRunner\n", "\n", "# Factory methods for creating multi-objective optimization modesl.\n", "from ax.modelbridge.factory import get_MOO_EHVI, get_MOO_PAREGO\n", "\n", "# Analysis utilities, including a method to evaluate hypervolumes\n", "from ax.modelbridge.modelbridge_utils import observed_hypervolume" ] }, { "cell_type": "markdown", "metadata": { "originalKey": "0b43c263-41da-4aa8-99f3-4a2a7fc49e4b" }, "source": [ "## Define experiment configurations" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "963a036d-a250-4e3c-9570-afe6f2192f9a" }, "source": [ "### Search Space" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:35.541270Z", "iopub.status.busy": "2023-08-11T16:08:35.541029Z", "iopub.status.idle": "2023-08-11T16:08:35.544669Z", "shell.execute_reply": "2023-08-11T16:08:35.544168Z" }, "executionStartTime": 1628191313915, "executionStopTime": 1628191313944, "hidden_ranges": [], "originalKey": "90637eb4-730f-4f3d-8712-875bf88d6c2d", "requestMsgId": "fbb9db8e-5414-4add-ad10-0bd00583ebf5" }, "outputs": [], "source": [ "x1 = RangeParameter(name=\"x1\", lower=0, upper=1, parameter_type=ParameterType.FLOAT)\n", "x2 = RangeParameter(name=\"x2\", lower=0, upper=1, parameter_type=ParameterType.FLOAT)\n", "\n", "search_space = SearchSpace(\n", " parameters=[x1, x2],\n", ")" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ac3cf1fe-d39d-48bb-a31d-e3ee0d70418b", "showInput": false }, "source": [ "### MultiObjectiveOptimizationConfig\n", "\n", "To optimize multiple objective we must create a `MultiObjective` containing the metrics we'll optimize and `MultiObjectiveOptimizationConfig` (which contains `ObjectiveThreshold`s) instead of our more typical `Objective` and `OptimizationConfig`\n", "\n", "We define `NoisyFunctionMetric`s to wrap our synthetic Branin-Currin problem's outputs. Add noise to see how robust our different optimization algorithms are." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:35.547492Z", "iopub.status.busy": "2023-08-11T16:08:35.547260Z", "iopub.status.idle": "2023-08-11T16:08:35.551818Z", "shell.execute_reply": "2023-08-11T16:08:35.551264Z" }, "executionStartTime": 1628191319191, "executionStopTime": 1628191319220, "hidden_ranges": [], "originalKey": "9fdb11b6-7845-4f06-90fd-527fee088d76", "requestMsgId": "febe0d60-fe60-4d55-ba6f-724c8ce7601d" }, "outputs": [], "source": [ "class MetricA(NoisyFunctionMetric):\n", " def f(self, x: np.ndarray) -> float:\n", " return float(branin_currin(torch.tensor(x))[0])\n", "\n", "\n", "class MetricB(NoisyFunctionMetric):\n", " def f(self, x: np.ndarray) -> float:\n", " return float(branin_currin(torch.tensor(x))[1])\n", "\n", "\n", "metric_a = MetricA(\"a\", [\"x1\", \"x2\"], noise_sd=0.0, lower_is_better=False)\n", "metric_b = MetricB(\"b\", [\"x1\", \"x2\"], noise_sd=0.0, lower_is_better=False)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:35.554404Z", "iopub.status.busy": "2023-08-11T16:08:35.554193Z", "iopub.status.idle": "2023-08-11T16:08:35.557282Z", "shell.execute_reply": "2023-08-11T16:08:35.556711Z" }, "executionStartTime": 1628191321755, "executionStopTime": 1628191321791, "hidden_ranges": [], "originalKey": "27065b03-7234-49c1-b3ae-f6442ec4e3d6", "requestMsgId": "d4010fca-5cbd-4a41-a779-cfa97ec15cc3" }, "outputs": [], "source": [ "mo = MultiObjective(\n", " objectives=[Objective(metric=metric_a), Objective(metric=metric_b)],\n", ")" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2023-08-11T16:08:35.559632Z", "iopub.status.busy": "2023-08-11T16:08:35.559437Z", "iopub.status.idle": "2023-08-11T16:08:35.562437Z", "shell.execute_reply": "2023-08-11T16:08:35.562004Z" }, "executionStartTime": 1628191323464, "executionStopTime": 1628191323491, "originalKey": "c58b70de-06b5-4e03-8958-c3c55d4c295a", "requestMsgId": "27e7efe5-d29e-4211-944e-41e6de065299" }, "outputs": [], "source": [ "objective_thresholds = [\n", " ObjectiveThreshold(metric=metric, bound=val, relative=False)\n", " for metric, val in zip(mo.metrics, branin_currin.ref_point)\n", "]" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:35.564747Z", "iopub.status.busy": "2023-08-11T16:08:35.564552Z", "iopub.status.idle": "2023-08-11T16:08:35.567241Z", "shell.execute_reply": "2023-08-11T16:08:35.566776Z" }, "executionStartTime": 1628191325491, "executionStopTime": 1628191325519, "hidden_ranges": [], "originalKey": "4b1ce9ba-e2e5-4a8a-9c15-5d01a2940a55", "requestMsgId": "314ea591-0d2e-4fb5-b091-2aa2ea27f0eb" }, "outputs": [], "source": [ "optimization_config = MultiObjectiveOptimizationConfig(\n", " objective=mo,\n", " objective_thresholds=objective_thresholds,\n", ")" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "3b7b797c-2478-48d6-84ea-c62a886db31f", "showInput": false }, "source": [ "## Define experiment creation utilities\n", "\n", "These construct our experiment, then initialize with Sobol points before we fit a Gaussian Process model to those initial points." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2023-08-11T16:08:35.569722Z", "iopub.status.busy": "2023-08-11T16:08:35.569531Z", "iopub.status.idle": "2023-08-11T16:08:35.572867Z", "shell.execute_reply": "2023-08-11T16:08:35.571878Z" }, "executionStartTime": 1628191328765, "executionStopTime": 1628191328792, "originalKey": "a52ace6c-8144-446b-97d5-2f27879ca187", "requestMsgId": "6a222fb5-231e-4476-86a6-c29ca5113332" }, "outputs": [], "source": [ "# Reasonable defaults for number of quasi-random initialization points and for subsequent model-generated trials.\n", "N_INIT = 6\n", "N_BATCH = 25" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:35.575360Z", "iopub.status.busy": "2023-08-11T16:08:35.575160Z", "iopub.status.idle": "2023-08-11T16:08:35.578276Z", "shell.execute_reply": "2023-08-11T16:08:35.577755Z" }, "executionStartTime": 1628191330913, "executionStopTime": 1628191330991, "hidden_ranges": [], "originalKey": "9fd6ec68-4c53-4276-a98a-61431cdc05d5", "requestMsgId": "8f659995-6b8f-4544-8392-03daaf8220b8" }, "outputs": [], "source": [ "def build_experiment():\n", " experiment = Experiment(\n", " name=\"pareto_experiment\",\n", " search_space=search_space,\n", " optimization_config=optimization_config,\n", " runner=SyntheticRunner(),\n", " )\n", " return experiment" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:35.582377Z", "iopub.status.busy": "2023-08-11T16:08:35.582016Z", "iopub.status.idle": "2023-08-11T16:08:35.586470Z", "shell.execute_reply": "2023-08-11T16:08:35.585589Z" }, "executionStartTime": 1628191334273, "executionStopTime": 1628191334299, "hidden_ranges": [], "originalKey": "a8eef6a6-1d53-494a-907f-10ca35492a8c", "requestMsgId": "b207dbd4-0a53-4efd-bbb9-9dee8835d60b" }, "outputs": [], "source": [ "## Initialize with Sobol samples\n", "\n", "\n", "def initialize_experiment(experiment):\n", " sobol = Models.SOBOL(search_space=experiment.search_space, seed=1234)\n", "\n", " for _ in range(N_INIT):\n", " experiment.new_trial(sobol.gen(1)).run()\n", "\n", " return experiment.fetch_data()" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "0c918735-9fda-4c36-90b5-163443e66c72", "showInput": false }, "source": [ "# Sobol\n", "We use quasirandom points as a fast baseline for evaluating the quality of our multi-objective optimization algorithms." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:35.589437Z", "iopub.status.busy": "2023-08-11T16:08:35.589191Z", "iopub.status.idle": "2023-08-11T16:08:35.663394Z", "shell.execute_reply": "2023-08-11T16:08:35.662701Z" }, "executionStartTime": 1628191356513, "executionStopTime": 1628191356896, "hidden_ranges": [], "originalKey": "5ee13832-804a-413f-a6bc-1f8f96a817d8", "requestMsgId": "5b40f1e6-45b9-40e4-8569-9d459e98ca57" }, "outputs": [], "source": [ "sobol_experiment = build_experiment()\n", "sobol_data = initialize_experiment(sobol_experiment)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:35.666734Z", "iopub.status.busy": "2023-08-11T16:08:35.666494Z", "iopub.status.idle": "2023-08-11T16:08:43.661157Z", "shell.execute_reply": "2023-08-11T16:08:43.660406Z" }, "executionStartTime": 1628191362562, "executionStopTime": 1628191408255, "hidden_ranges": [], "originalKey": "0c6a6d44-29db-43dd-982d-dc664d00b009", "requestMsgId": "8aca7b5b-aab8-4a39-9a49-d7b1e0c714c5" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 0, HV: 12.851780072837377\n", "Iteration: 1, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 2, HV: 12.851780072837377\n", "Iteration: 3, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 4, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 5, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 6, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 7, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 8, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 9, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 10, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 11, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 12, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 13, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 14, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 15, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 16, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 17, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 18, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 19, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 20, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 21, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 22, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 23, HV: 12.851780072837377\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 12.851780072837377\n" ] } ], "source": [ "sobol_model = Models.SOBOL(\n", " experiment=sobol_experiment,\n", " data=sobol_data,\n", ")\n", "sobol_hv_list = []\n", "for i in range(N_BATCH):\n", " generator_run = sobol_model.gen(1)\n", " trial = sobol_experiment.new_trial(generator_run=generator_run)\n", " trial.run()\n", " exp_df = exp_to_df(sobol_experiment)\n", " outcomes = np.array(exp_df[[\"a\", \"b\"]], dtype=np.double)\n", " # Fit a GP-based model in order to calculate hypervolume.\n", " # We will not use this model to generate new points.\n", " dummy_model = get_MOO_EHVI(\n", " experiment=sobol_experiment,\n", " data=sobol_experiment.fetch_data(),\n", " )\n", " try:\n", " hv = observed_hypervolume(modelbridge=dummy_model)\n", " except:\n", " hv = 0\n", " print(\"Failed to compute hv\")\n", " sobol_hv_list.append(hv)\n", " print(f\"Iteration: {i}, HV: {hv}\")\n", "\n", "sobol_outcomes = np.array(exp_to_df(sobol_experiment)[[\"a\", \"b\"]], dtype=np.double)" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "767a7e9b-8902-424e-bfc4-f7afdba47302" }, "source": [ "## qNEHVI\n", "Noisy Expected Hypervolume Improvement. This is our current recommended algorithm for multi-objective optimization." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:43.664937Z", "iopub.status.busy": "2023-08-11T16:08:43.664437Z", "iopub.status.idle": "2023-08-11T16:08:43.738859Z", "shell.execute_reply": "2023-08-11T16:08:43.737947Z" }, "executionStartTime": 1628191422463, "executionStopTime": 1628191422803, "hidden_ranges": [], "originalKey": "8fc6bfb4-3012-4ce2-99ed-288378098c50", "requestMsgId": "0fd945a2-ac45-4a74-82cc-7173e15ced85" }, "outputs": [], "source": [ "ehvi_experiment = build_experiment()\n", "ehvi_data = initialize_experiment(ehvi_experiment)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:08:43.742430Z", "iopub.status.busy": "2023-08-11T16:08:43.742149Z", "iopub.status.idle": "2023-08-11T16:09:11.876843Z", "shell.execute_reply": "2023-08-11T16:09:11.876151Z" }, "executionStartTime": 1628191425090, "executionStopTime": 1628191500240, "hidden_ranges": [], "originalKey": "27dd9425-b77e-4027-8412-30dd40c5abf1", "requestMsgId": "65430b82-de1e-4946-9d8d-4a75762354c1" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 0, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 1, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 2, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 3, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 4, HV: 2.369795709893773\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 5, HV: 23.290889973823354\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 6, HV: 34.2937448832927\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 7, HV: 40.2495329521432\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 8, HV: 45.38842854380693\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 9, HV: 48.93750247805157\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 10, HV: 51.12110514887196\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 11, HV: 52.047779988611126\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 12, HV: 52.877139615244744\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 13, HV: 54.11694384636843\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 14, HV: 54.76723018192303\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 15, HV: 55.422244569282114\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 16, HV: 55.49091628531845\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 17, HV: 55.78643272799068\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 18, HV: 56.000181445812444\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 19, HV: 56.30111376222678\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 20, HV: 56.49497927254365\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 21, HV: 56.79765036492464\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 22, HV: 56.95137390810647\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 23, HV: 57.10487755168474\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 57.15910770899022\n" ] } ], "source": [ "ehvi_hv_list = []\n", "ehvi_model = None\n", "for i in range(N_BATCH):\n", " ehvi_model = get_MOO_EHVI(\n", " experiment=ehvi_experiment,\n", " data=ehvi_data,\n", " )\n", " generator_run = ehvi_model.gen(1)\n", " trial = ehvi_experiment.new_trial(generator_run=generator_run)\n", " trial.run()\n", " ehvi_data = Data.from_multiple_data([ehvi_data, trial.fetch_data()])\n", "\n", " exp_df = exp_to_df(ehvi_experiment)\n", " outcomes = np.array(exp_df[[\"a\", \"b\"]], dtype=np.double)\n", " try:\n", " hv = observed_hypervolume(modelbridge=ehvi_model)\n", " except:\n", " hv = 0\n", " print(\"Failed to compute hv\")\n", " ehvi_hv_list.append(hv)\n", " print(f\"Iteration: {i}, HV: {hv}\")\n", "\n", "ehvi_outcomes = np.array(exp_to_df(ehvi_experiment)[[\"a\", \"b\"]], dtype=np.double)" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "e93178b6-5ba4-4c01-b8a2-e05971b7326f", "showInput": false }, "source": [ "## Plot qNEHVI Pareto Frontier based on model posterior \n", "\n", "The plotted points are samples from the fitted model's posterior, not observed samples." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:09:11.880253Z", "iopub.status.busy": "2023-08-11T16:09:11.879985Z", "iopub.status.idle": "2023-08-11T16:09:32.177152Z", "shell.execute_reply": "2023-08-11T16:09:32.176421Z" }, "executionStartTime": 1628191505148, "executionStopTime": 1628191521900, "hidden_ranges": [], "originalKey": "71e013c5-638f-4ba4-bb9a-3e4a7d3eb9fa", "requestMsgId": "681433c5-fc21-4699-9fe1-8e444c671153" }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "error_x": { "array": [ 0.07954370182786749, 0.07954370237456372, 0.04941116847031843, 0.07954370237456372, 0.0488480063357106, 0.04534046248054374, 0.05041698632336496, 0.04882127940743479, 0.0564935629522362, 0.04992633146551542, 0.053585644266762586, 0.049388220253117156, 0.04646185305991321, 0.049499372382779856, 0.049597007647021, 0.04509362095532813, 0.05332982005052478, 0.05013533581884392, 0.07122948480280804, 0.09204136176820622 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "error_y": { "array": [ 0.0037413567079564677, 0.003741356705785884, 0.002376825867570255, 0.003741356705785884, 0.002393672683875976, 0.002191985467902811, 0.0024186325009805045, 0.002378557843788321, 0.00260255294527614, 0.0024156026556492447, 0.002491486379951309, 0.0024164324328841036, 0.002282112836966302, 0.0024135775244245017, 0.00237924837598822, 0.002168880222310113, 0.0024825202944809, 0.0024160544176263653, 0.0031903594773119684, 0.0038286296804715815 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "hoverinfo": "text", "legendgroup": "mean", "marker": { "color": "rgba(128,177,211,1)" }, "mode": "markers", "name": "mean", "text": [ "Parameterization 0
a: -17.506 [-17.585, -17.426]
b: -1.18 [-1.184, -1.176]

Parameterization:
x1: 0.0
x2: 0.9999999999996698", "Parameterization 1
a: -17.506 [-17.585, -17.426]
b: -1.18 [-1.184, -1.176]

Parameterization:
x1: 0.0
x2: 1.0", "Parameterization 2
a: -15.535 [-15.584, -15.485]
b: -1.436 [-1.438, -1.433]

Parameterization:
x1: 0.0062363539773861365
x2: 0.9999999999999999", "Parameterization 3
a: -17.506 [-17.585, -17.426]
b: -1.18 [-1.184, -1.176]

Parameterization:
x1: 0.0
x2: 1.0", "Parameterization 4
a: -14.823 [-14.872, -14.774]
b: -1.532 [-1.534, -1.529]

Parameterization:
x1: 0.008595643296876239
x2: 1.0", "Parameterization 5
a: -7.207 [-7.253, -7.162]
b: -2.776 [-2.778, -2.774]

Parameterization:
x1: 0.04053580602507124
x2: 1.0", "Parameterization 6
a: -12.575 [-12.625, -12.524]
b: -1.852 [-1.855, -1.850]

Parameterization:
x1: 0.016525216765065093
x2: 1.0", "Parameterization 7
a: -15.175 [-15.224, -15.126]
b: -1.484 [-1.486, -1.482]

Parameterization:
x1: 0.007421583494703797
x2: 1.0", "Parameterization 8
a: -16.457 [-16.513, -16.400]
b: -1.314 [-1.317, -1.312]

Parameterization:
x1: 0.0032676942794239313
x2: 0.9999999999999999", "Parameterization 9
a: -11.771 [-11.821, -11.721]
b: -1.974 [-1.976, -1.972]

Parameterization:
x1: 0.019573636424066877
x2: 1.0", "Parameterization 10
a: -16.212 [-16.265, -16.158]
b: -1.346 [-1.349, -1.344]

Parameterization:
x1: 0.0040478046163218585
x2: 1.0", "Parameterization 11
a: -14.295 [-14.345, -14.246]
b: -1.605 [-1.607, -1.602]

Parameterization:
x1: 0.010388193496635353
x2: 1.0", "Parameterization 12
a: -9.404 [-9.450, -9.358]
b: -2.361 [-2.363, -2.359]

Parameterization:
x1: 0.029463433030784872
x2: 1.0", "Parameterization 13
a: -11.358 [-11.408, -11.309]
b: -2.038 [-2.041, -2.036]

Parameterization:
x1: 0.021192777840065832
x2: 1.0", "Parameterization 14
a: -15.595 [-15.644, -15.545]
b: -1.428 [-1.430, -1.425]

Parameterization:
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "frontier = compute_posterior_pareto_frontier(\n", " experiment=ehvi_experiment,\n", " data=ehvi_experiment.fetch_data(),\n", " primary_objective=metric_b,\n", " secondary_objective=metric_a,\n", " absolute_metrics=[\"a\", \"b\"],\n", " num_points=20,\n", ")\n", "\n", "render(plot_pareto_frontier(frontier, CI_level=0.90))" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "77b2dbce-f1e4-443a-8f81-2e1cbe207301" }, "source": [ "## qNParEGO\n", "This is a good alternative algorithm for multi-objective optimization when qNEHVI runs too slowly." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:09:32.180867Z", "iopub.status.busy": "2023-08-11T16:09:32.180592Z", "iopub.status.idle": "2023-08-11T16:09:32.266023Z", "shell.execute_reply": "2023-08-11T16:09:32.265371Z" }, "hidden_ranges": [], "originalKey": "2f796182-558b-47aa-8072-4dbf40123133" }, "outputs": [], "source": [ "parego_experiment = build_experiment()\n", "parego_data = initialize_experiment(parego_experiment)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:09:32.269358Z", "iopub.status.busy": "2023-08-11T16:09:32.269098Z", "iopub.status.idle": "2023-08-11T16:09:55.624892Z", "shell.execute_reply": "2023-08-11T16:09:55.624168Z" }, "hidden_ranges": [], "originalKey": "72999188-90f5-43e0-b1d9-d468e7d51191" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 0, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 1, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 2, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 3, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 4, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 5, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 6, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 7, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 8, HV: 2.3697957098937663\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 9, HV: 7.768961385366106\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 10, HV: 7.768961385366106\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 11, HV: 7.768961385366106\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 12, HV: 7.768961385366106\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 13, HV: 7.768961385366106\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 14, HV: 7.768961385366106\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 15, HV: 7.768961385366106\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 16, HV: 19.25446541744232\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 17, HV: 19.25446541744232\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 18, HV: 19.25446541744232\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 19, HV: 19.25446541744232\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 20, HV: 19.25446541744232\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 21, HV: 19.25446541744232\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 22, HV: 19.25446541744232\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 23, HV: 19.25446541744232\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 19.25446541744232\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/mpolson64/opt/anaconda3/envs/ax-dev/lib/python3.9/site-packages/botorch/optim/initializers.py:403: BadInitialCandidatesWarning:\n", "\n", "Unable to find non-zero acquisition function values - initial conditions are being selected randomly.\n", "\n" ] } ], "source": [ "parego_hv_list = []\n", "parego_model = None\n", "for i in range(N_BATCH):\n", " parego_model = get_MOO_PAREGO(\n", " experiment=parego_experiment,\n", " data=parego_data,\n", " )\n", " generator_run = parego_model.gen(1)\n", " trial = parego_experiment.new_trial(generator_run=generator_run)\n", " trial.run()\n", " parego_data = Data.from_multiple_data([parego_data, trial.fetch_data()])\n", "\n", " exp_df = exp_to_df(parego_experiment)\n", " outcomes = np.array(exp_df[[\"a\", \"b\"]], dtype=np.double)\n", " try:\n", " hv = observed_hypervolume(modelbridge=parego_model)\n", " except:\n", " hv = 0\n", " print(\"Failed to compute hv\")\n", " parego_hv_list.append(hv)\n", " print(f\"Iteration: {i}, HV: {hv}\")\n", "\n", "parego_outcomes = np.array(exp_to_df(parego_experiment)[[\"a\", \"b\"]], dtype=np.double)" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "67ded85f-7c58-4c31-8df5-b0d8d07e4299", "showInput": false }, "source": [ "## Plot qNParEGO Pareto Frontier based on model posterior \n", "\n", "The plotted points are samples from the fitted model's posterior, not observed samples." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:09:55.628218Z", "iopub.status.busy": "2023-08-11T16:09:55.627960Z", "iopub.status.idle": "2023-08-11T16:10:14.122856Z", "shell.execute_reply": "2023-08-11T16:10:14.122058Z" }, "hidden_ranges": [], "originalKey": "3b1f39fd-ef75-4ea4-865b-f7b54b90da07" }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "error_x": { "array": [ 0.09138707072276077, 0.09138707072276077, 0.07442731705715595, 0.09138707083445223, 0.2335704054393958, 0.0724260042951255, 0.08751934751217302, 0.12797355276135958, 0.11013709778944987, 0.2164618952560504, 0.3095798931250234, 0.20402126791095618, 0.24093977743530265, 0.20191356105874853, 0.0913870706110693, 0.3264158639696272, 0.07876065800089717, 0.3367671453626832, 0.08141233968789045, 0.9903677339929553 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "error_y": { "array": [ 0.004527043034041546, 0.0045270430289982904, 0.0035822174998617604, 0.004527043034041546, 0.015768969101532106, 0.004188345689098596, 0.004436024326786003, 0.0067085509291197375, 0.005345627941511751, 0.014294375028526334, 0.022291173961101154, 0.013220437208510478, 0.016403301206125796, 0.013038363204440694, 0.004527043036563174, 0.023731040939215887, 0.0046114824210598876, 0.024615722640174795, 0.004575796770885941, 0.08043842578096154 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "hoverinfo": "text", "legendgroup": "mean", "marker": { "color": "rgba(128,177,211,1)" }, "mode": "markers", "name": "mean", "text": [ "Parameterization 0
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "frontier = compute_posterior_pareto_frontier(\n", " experiment=parego_experiment,\n", " data=parego_experiment.fetch_data(),\n", " primary_objective=metric_b,\n", " secondary_objective=metric_a,\n", " absolute_metrics=[\"a\", \"b\"],\n", " num_points=20,\n", ")\n", "\n", "render(plot_pareto_frontier(frontier, CI_level=0.90))" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "collapsed": true, "hidden_ranges": [], "originalKey": "a67f7345-1777-4372-8704-bb80c4c4e783" }, "source": [ "## Plot empirical data" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "collapsed": true, "hidden_ranges": [], "originalKey": "de878adc-0eb2-4599-8c1b-e0adbc0c0765", "showInput": false }, "source": [ "#### Plot observed hypervolume, with color representing the iteration that a point was generated on.\n", "\n", "To examine optimization process from another perspective, we plot the collected observations under each algorithm where the color corresponds to the BO iteration at which the point was collected. The plot on the right for $q$NEHVI shows that the $q$NEHVI quickly identifies the Pareto frontier and most of its evaluations are very close to the Pareto frontier. $q$NParEGO also identifies has many observations close to the Pareto frontier, but relies on optimizing random scalarizations, which is a less principled way of optimizing the Pareto front compared to $q$NEHVI, which explicitly attempts focuses on improving the Pareto front. Sobol generates random points and has few points close to the Pareto front." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:10:14.128440Z", "iopub.status.busy": "2023-08-11T16:10:14.128110Z", "iopub.status.idle": "2023-08-11T16:10:16.662261Z", "shell.execute_reply": "2023-08-11T16:10:16.661642Z" }, "hidden_ranges": [], "originalKey": "c6296697-ef07-422d-b965-35e4e5104a12" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/w_/g_40lr6j0s98g6921f3qxcmr0000gn/T/ipykernel_52355/1991852771.py:11: MatplotlibDeprecationWarning:\n", "\n", "The get_cmap function was deprecated in Matplotlib 3.7 and will be removed two minor releases later. Use ``matplotlib.colormaps[name]`` or ``matplotlib.colormaps.get_cmap(obj)`` instead.\n", "\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'Iteration')" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "%matplotlib inline\n", "\n", "from matplotlib.cm import ScalarMappable\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(20, 6))\n", "algos = [\"Sobol\", \"qNParEGO\", \"qNEHVI\"]\n", "outcomes_list = [sobol_outcomes, parego_outcomes, ehvi_outcomes]\n", "cm = plt.cm.get_cmap(\"viridis\")\n", "BATCH_SIZE = 1\n", "\n", "n_results = N_BATCH * BATCH_SIZE + N_INIT\n", "batch_number = torch.cat(\n", " [\n", " torch.zeros(N_INIT),\n", " torch.arange(1, N_BATCH + 1).repeat(BATCH_SIZE, 1).t().reshape(-1),\n", " ]\n", ").numpy()\n", "for i, train_obj in enumerate(outcomes_list):\n", " x = i\n", " sc = axes[x].scatter(\n", " train_obj[:n_results, 0],\n", " train_obj[:n_results, 1],\n", " c=batch_number[:n_results],\n", " alpha=0.8,\n", " )\n", " axes[x].set_title(algos[i])\n", " axes[x].set_xlabel(\"Objective 1\")\n", " axes[x].set_xlim(-150, 5)\n", " axes[x].set_ylim(-15, 0)\n", "axes[0].set_ylabel(\"Objective 2\")\n", "norm = plt.Normalize(batch_number.min(), batch_number.max())\n", "sm = ScalarMappable(norm=norm, cmap=cm)\n", "sm.set_array([])\n", "fig.subplots_adjust(right=0.9)\n", "cbar_ax = fig.add_axes([0.93, 0.15, 0.01, 0.7])\n", "cbar = fig.colorbar(sm, cax=cbar_ax)\n", "cbar.ax.set_title(\"Iteration\")" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ca12287f-c7b8-4ef8-8eb9-57760eda5fed", "showInput": true }, "source": [ "# Hypervolume statistics\n", "The hypervolume of the space dominated by points that dominate the reference point." ] }, { "cell_type": "markdown", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ec8b764b-c27d-4722-9e3d-d81cebb3624a" }, "source": [ "#### Plot the results\n", "The plot below shows a common metric of multi-objective optimization performance when the true Pareto frontier is known: the log difference between the hypervolume of the true Pareto front and the hypervolume of the approximate Pareto front identified by each algorithm. The log hypervolume difference is plotted at each step of the optimization for each of the algorithms.\n", "\n", "The plot show that $q$NEHVI vastly outperforms $q$NParEGO which outperforms the Sobol baseline." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2023-08-11T16:10:16.665473Z", "iopub.status.busy": "2023-08-11T16:10:16.665136Z", "iopub.status.idle": "2023-08-11T16:10:16.883692Z", "shell.execute_reply": "2023-08-11T16:10:16.883065Z" }, "hidden_ranges": [], "originalKey": "d50b98bc-5ab1-4826-a5b2-474a13f4bae0" }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "%matplotlib inline\n", "\n", "iters = np.arange(1, N_BATCH + 1)\n", "log_hv_difference_sobol = np.log10(branin_currin.max_hv - np.asarray(sobol_hv_list))[\n", " : N_BATCH + 1\n", "]\n", "log_hv_difference_parego = np.log10(branin_currin.max_hv - np.asarray(parego_hv_list))[\n", " : N_BATCH + 1\n", "]\n", "log_hv_difference_ehvi = np.log10(branin_currin.max_hv - np.asarray(ehvi_hv_list))[\n", " : N_BATCH + 1\n", "]\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(8, 6))\n", "ax.plot(iters, log_hv_difference_sobol, label=\"Sobol\", linewidth=1.5)\n", "ax.plot(iters, log_hv_difference_parego, label=\"qNParEGO\", linewidth=1.5)\n", "ax.plot(iters, log_hv_difference_ehvi, label=\"qNEHVI\", linewidth=1.5)\n", "ax.set(\n", " xlabel=\"number of observations (beyond initial points)\",\n", " ylabel=\"Log Hypervolume Difference\",\n", ")\n", "ax.legend(loc=\"lower right\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.17" } }, "nbformat": 4, "nbformat_minor": 2 }