{ "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": "2022-09-15T18:15:18.214436Z", "iopub.status.busy": "2022-09-15T18:15:18.214069Z", "iopub.status.idle": "2022-09-15T18:15:21.002015Z", "shell.execute_reply": "2022-09-15T18:15:21.001017Z" }, "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 09-15 18:15:20] 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", "init_notebook_plotting()\n", "\n", "# Load our sample 2-objective problem\n", "from botorch.test_functions.multi_objective import BraninCurrin\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": "2022-09-15T18:15:21.077713Z", "iopub.status.busy": "2022-09-15T18:15:21.076932Z", "iopub.status.idle": "2022-09-15T18:15:21.092385Z", "shell.execute_reply": "2022-09-15T18:15:21.091422Z" }, "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 09-15 18:15:21] 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 09-15 18:15:21] 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 09-15 18:15:21] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] 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 09-15 18:15:21] 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 09-15 18:15:21] ax.modelbridge.dispatch_utils: Using Bayesian optimization since there are more ordered parameters than there are categories for the unordered categorical parameters.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] 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": "2022-09-15T18:15:21.096941Z", "iopub.status.busy": "2022-09-15T18:15:21.096061Z", "iopub.status.idle": "2022-09-15T18:15:21.102273Z", "shell.execute_reply": "2022-09-15T18:15:21.101369Z" }, "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(torch.tensor([parameters.get(\"x1\"), parameters.get(\"x2\")]))\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": "2022-09-15T18:15:21.106414Z", "iopub.status.busy": "2022-09-15T18:15:21.106105Z", "iopub.status.idle": "2022-09-15T18:15:57.505741Z", "shell.execute_reply": "2022-09-15T18:15:57.502637Z" }, "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 09-15 18:15:21] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.218453, 'x2': 0.988708}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Completed trial 0 with data: {'a': (-41.082893, 0.0), 'b': (-5.476907, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.293812, 'x2': 0.422865}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Completed trial 1 with data: {'a': (-18.380924, 0.0), 'b': (-9.301629, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.113798, 'x2': 0.446146}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Completed trial 2 with data: {'a': (-35.906948, 0.0), 'b': (-8.115517, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.546607, 'x2': 0.050682}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Completed trial 3 with data: {'a': (-2.57568, 0.0), 'b': (-11.424207, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.056196, 'x2': 0.450709}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Completed trial 4 with data: {'a': (-70.353142, 0.0), 'b': (-5.650499, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.496312, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:21] ax.service.ax_client: Completed trial 5 with data: {'a': (-149.501205, 0.0), 'b': (-4.61914, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:22] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.0, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:22] ax.service.ax_client: Completed trial 6 with data: {'a': (-17.508297, 0.0), 'b': (-1.180408, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:23] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.033534, 'x2': 0.86499}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:23] ax.service.ax_client: Completed trial 7 with data: {'a': (-15.758657, 0.0), 'b': (-2.807406, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:24] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.063436, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:24] ax.service.ax_client: Completed trial 8 with data: {'a': (-4.27605, 0.0), 'b': (-3.546853, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:24] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 1.0, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:24] ax.service.ax_client: Completed trial 9 with data: {'a': (-145.872208, 0.0), 'b': (-4.005316, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:25] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 1.0, 'x2': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:25] ax.service.ax_client: Completed trial 10 with data: {'a': (-10.960894, 0.0), 'b': (-10.179487, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:27] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.028861, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:27] ax.service.ax_client: Completed trial 11 with data: {'a': (-9.537551, 0.0), 'b': (-2.338013, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:29] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.08138, 'x2': 0.936681}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:29] ax.service.ax_client: Completed trial 12 with data: {'a': (-2.321183, 0.0), 'b': (-4.261325, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:32] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.013901, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:32] ax.service.ax_client: Completed trial 13 with data: {'a': (-13.292375, 0.0), 'b': (-1.746555, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:32] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.77717, 'x2': 0.614695}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:32] ax.service.ax_client: Completed trial 14 with data: {'a': (-84.391747, 0.0), 'b': (-5.854741, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:36] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.044011, 'x2': 0.996155}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:36] ax.service.ax_client: Completed trial 15 with data: {'a': (-6.66305, 0.0), 'b': (-2.909425, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:39] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.102466, 'x2': 0.878375}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:39] ax.service.ax_client: Completed trial 16 with data: {'a': (-0.902817, 0.0), 'b': (-4.999219, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:40] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.006819, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:40] ax.service.ax_client: Completed trial 17 with data: {'a': (-15.355672, 0.0), 'b': (-1.459134, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:42] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 1.0, 'x2': 0.518149}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:42] ax.service.ax_client: Completed trial 18 with data: {'a': (-24.689133, 0.0), 'b': (-6.301171, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:44] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.052762, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:44] ax.service.ax_client: Completed trial 19 with data: {'a': (-5.364499, 0.0), 'b': (-3.203535, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:46] ax.service.ax_client: Generated new trial 20 with parameters {'x1': 0.071578, 'x2': 0.965809}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:46] ax.service.ax_client: Completed trial 20 with data: {'a': (-3.266678, 0.0), 'b': (-3.890508, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:48] ax.service.ax_client: Generated new trial 21 with parameters {'x1': 0.036197, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:48] ax.service.ax_client: Completed trial 21 with data: {'a': (-8.010183, 0.0), 'b': (-2.616034, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:50] ax.service.ax_client: Generated new trial 22 with parameters {'x1': 0.091266, 'x2': 0.909952}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:50] ax.service.ax_client: Completed trial 22 with data: {'a': (-1.553032, 0.0), 'b': (-4.613123, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:53] ax.service.ax_client: Generated new trial 23 with parameters {'x1': 0.114316, 'x2': 0.839663}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:53] ax.service.ax_client: Completed trial 23 with data: {'a': (-0.497588, 0.0), 'b': (-5.412943, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:57] ax.service.ax_client: Generated new trial 24 with parameters {'x1': 0.021136, 'x2': 1.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 09-15 18:15:57] ax.service.ax_client: Completed trial 24 with data: {'a': (-11.371858, 0.0), 'b': (-2.035969, 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": "2022-09-15T18:15:57.510721Z", "iopub.status.busy": "2022-09-15T18:15:57.510229Z", "iopub.status.idle": "2022-09-15T18:16:08.622264Z", "shell.execute_reply": "2022-09-15T18:16:08.621290Z" }, "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": [ 0.031993625812058966, 0.02627764289439352, 0.05213938509812331, 0.02624640464363012, 0.031993625812058966, 0.03681617131819854, 0.02672083560201969, 0.04096471959163306, 0.03199362579580539, 0.03199362582831255, 0.03199362584456612, 0.030867149569844404, 0.03199362582831255, 0.02163792783707258, 0.03199362584456612, 0.037479587249713724, 0.031993625812058966, 0.031993625812058966, 0.025550098098847358, 0.042210476728909783 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "error_y": { "array": [ 0.002073996009403589, 0.0016360336400919754, 0.002999479304690764, 0.0016813622992642857, 0.002073996010456068, 0.0021238383055486444, 0.001698570669737131, 0.0023145068006526592, 0.002073996011508547, 0.002073996010456068, 0.0020739960125610263, 0.0018900853236411353, 0.002073996010456068, 0.001406315667673669, 0.002073996010456068, 0.002158636327292815, 0.002073996010456068, 0.002073996010456068, 0.001581137244351337, 0.0024160750707003615 ], "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
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.538, -17.474]

Parameterization:
x1: 1.0675856091067774e-16
x2: 1.0", "Parameterization 1
b: -3.448 [-3.450, -3.446]
a: -4.545 [-4.571, -4.518]

Parameterization:
x1: 0.060014382081816864
x2: 0.9969411290518013", "Parameterization 2
b: -5.062 [-5.065, -5.059]
a: -0.815 [-0.867, -0.763]

Parameterization:
x1: 0.1048126348111181
x2: 0.8755259612813577", "Parameterization 3
b: -3.394 [-3.396, -3.393]
a: -4.71 [-4.736, -4.684]

Parameterization:
x1: 0.05858518529111561
x2: 1.0", "Parameterization 4
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.538, -17.474]

Parameterization:
x1: 3.415591509587361e-17
x2: 1.0", "Parameterization 5
b: -4.564 [-4.566, -4.562]
a: -1.649 [-1.686, -1.612]

Parameterization:
x1: 0.09018069450128988
x2: 0.9159917059623885", "Parameterization 6
b: -3.278 [-3.280, -3.277]
a: -5.095 [-5.122, -5.069]

Parameterization:
x1: 0.055014886689710614
x2: 1.0", "Parameterization 7
b: -4.791 [-4.794, -4.789]
a: -1.223 [-1.264, -1.182]

Parameterization:
x1: 0.09675338975843248
x2: 0.8979857540151469", "Parameterization 8
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.538, -17.474]

Parameterization:
x1: 4.819774439066036e-15
x2: 0.9999999999999857", "Parameterization 9
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.538, -17.474]

Parameterization:
x1: 0.0
x2: 1.0", "Parameterization 10
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.538, -17.474]

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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": "2022-09-15T18:16:08.627684Z", "iopub.status.busy": "2022-09-15T18:16:08.626903Z", "iopub.status.idle": "2022-09-15T18:16:08.632745Z", "shell.execute_reply": "2022-09-15T18:16:08.631817Z" }, "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.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": "2022-09-15T18:16:08.637921Z", "iopub.status.busy": "2022-09-15T18:16:08.637455Z", "iopub.status.idle": "2022-09-15T18:16:08.643012Z", "shell.execute_reply": "2022-09-15T18:16:08.642095Z" }, "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": "2022-09-15T18:16:08.647283Z", "iopub.status.busy": "2022-09-15T18:16:08.646519Z", "iopub.status.idle": "2022-09-15T18:16:08.653308Z", "shell.execute_reply": "2022-09-15T18:16:08.652414Z" }, "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", "class MetricB(NoisyFunctionMetric):\n", " def f(self, x: np.ndarray) -> float:\n", " return float(branin_currin(torch.tensor(x))[1])\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": "2022-09-15T18:16:08.657302Z", "iopub.status.busy": "2022-09-15T18:16:08.656536Z", "iopub.status.idle": "2022-09-15T18:16:08.661080Z", "shell.execute_reply": "2022-09-15T18:16:08.660122Z" }, "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": "2022-09-15T18:16:08.665187Z", "iopub.status.busy": "2022-09-15T18:16:08.664840Z", "iopub.status.idle": "2022-09-15T18:16:08.669959Z", "shell.execute_reply": "2022-09-15T18:16:08.668925Z" }, "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": "2022-09-15T18:16:08.674122Z", "iopub.status.busy": "2022-09-15T18:16:08.673806Z", "iopub.status.idle": "2022-09-15T18:16:08.678127Z", "shell.execute_reply": "2022-09-15T18:16:08.677055Z" }, "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": "2022-09-15T18:16:08.682454Z", "iopub.status.busy": "2022-09-15T18:16:08.682112Z", "iopub.status.idle": "2022-09-15T18:16:08.686263Z", "shell.execute_reply": "2022-09-15T18:16:08.685245Z" }, "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": "2022-09-15T18:16:08.690562Z", "iopub.status.busy": "2022-09-15T18:16:08.690010Z", "iopub.status.idle": "2022-09-15T18:16:08.694715Z", "shell.execute_reply": "2022-09-15T18:16:08.693805Z" }, "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": "2022-09-15T18:16:08.698896Z", "iopub.status.busy": "2022-09-15T18:16:08.698314Z", "iopub.status.idle": "2022-09-15T18:16:08.704942Z", "shell.execute_reply": "2022-09-15T18:16:08.704127Z" }, "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", "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": "2022-09-15T18:16:08.709774Z", "iopub.status.busy": "2022-09-15T18:16:08.709274Z", "iopub.status.idle": "2022-09-15T18:16:08.895353Z", "shell.execute_reply": "2022-09-15T18:16:08.894300Z" }, "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": "2022-09-15T18:16:08.899864Z", "iopub.status.busy": "2022-09-15T18:16:08.899455Z", "iopub.status.idle": "2022-09-15T18:16:27.450990Z", "shell.execute_reply": "2022-09-15T18:16:27.449916Z" }, "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: 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: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 9, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 10, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 11, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 12, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 13, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 14, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 15, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 16, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 17, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 18, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 19, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 20, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 21, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 22, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 23, HV: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 0.0\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": "2022-09-15T18:16:27.455416Z", "iopub.status.busy": "2022-09-15T18:16:27.454774Z", "iopub.status.idle": "2022-09-15T18:16:27.638642Z", "shell.execute_reply": "2022-09-15T18:16:27.637514Z" }, "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": "2022-09-15T18:16:27.643184Z", "iopub.status.busy": "2022-09-15T18:16:27.642775Z", "iopub.status.idle": "2022-09-15T18:17:42.484681Z", "shell.execute_reply": "2022-09-15T18:17:42.483289Z" }, "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: 23.918469533389725\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 6, HV: 33.34017885502789\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 7, HV: 40.82940526575332\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 8, HV: 45.50463363523417\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 9, HV: 48.9666834717153\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 10, HV: 50.71176329588486\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 11, HV: 52.50414083440374\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 12, HV: 53.266735559062425\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 13, HV: 54.31702198894373\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 14, HV: 54.75292550395552\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 15, HV: 55.184349825096746\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 16, HV: 55.234409910486434\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 17, HV: 55.53119600407443\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 18, HV: 55.94046667665131\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 19, HV: 56.35061669969046\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 20, HV: 56.62653501723055\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 21, HV: 56.87570468689282\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 22, HV: 56.93982361066617\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 23, HV: 57.045650012465444\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 57.14566174404692\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": "2022-09-15T18:17:42.489316Z", "iopub.status.busy": "2022-09-15T18:17:42.489006Z", "iopub.status.idle": "2022-09-15T18:17:53.911456Z", "shell.execute_reply": "2022-09-15T18:17:53.910430Z" }, "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": [ 0.041069929096409975, 0.041069929096409975, 0.04106992904818858, 0.041069929096409975, 0.023019585107335025, 0.04106992931340626, 0.041069929168742074, 0.041069929096409975, 0.04106992907229928, 0.041069929168742074, 0.036117309209212675, 0.04106992904818858, 0.027624003325171585, 0.04250767113244075, 0.041069929096409975, 0.03586540882391687, 0.021238747315228738, 0.04106992902407789, 0.03620645704159947, 0.04106992933751695 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "error_y": { "array": [ 0.0019332630694322095, 0.0019332630704941409, 0.001933263072618003, 0.0019332630704941409, 0.0011004021288698118, 0.0019332630619986909, 0.001933263067308347, 0.0019332630704941409, 0.0019332630715560716, 0.0019332630651844845, 0.001574352942181143, 0.001933263072618003, 0.0013080405861118916, 0.0018487727645574118, 0.001933263067308347, 0.0016063016248144997, 0.0010248338544168055, 0.0019332630683702784, 0.0015770391872031394, 0.001933263067308347 ], "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
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 0.0
x2: 1.0", "Parameterization 1
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 2.68302837666376e-19
x2: 0.9999999999999999", "Parameterization 2
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 0.0
x2: 0.9999999999999994", "Parameterization 3
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 0.0
x2: 0.9999999999999999", "Parameterization 4
b: -1.924 [-1.925, -1.922]
a: -12.1 [-12.123, -12.077]

Parameterization:
x1: 0.01830937737326368
x2: 1.0", "Parameterization 5
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 0.0
x2: 0.9999999999935086", "Parameterization 6
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 2.305195452350942e-17
x2: 0.9999999999999901", "Parameterization 7
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 0.0
x2: 0.9999999999999999", "Parameterization 8
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 7.949288854630158e-17
x2: 1.0", "Parameterization 9
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 2.4757192833645426e-14
x2: 0.9999999999999836", "Parameterization 10
b: -3.944 [-3.946, -3.943]
a: -3.121 [-3.157, -3.085]

Parameterization:
x1: 0.07311713677732863
x2: 0.9629464004689735", "Parameterization 11
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 0.0
x2: 0.9999999999999994", "Parameterization 12
b: -1.369 [-1.371, -1.368]
a: -16.035 [-16.063, -16.007]

Parameterization:
x1: 0.004614043954205236
x2: 1.0", "Parameterization 13
b: -4.505 [-4.507, -4.503]
a: -1.762 [-1.805, -1.720]

Parameterization:
x1: 0.08856819519988136
x2: 0.921010838710802", "Parameterization 14
b: -1.18 [-1.182, -1.178]
a: -17.506 [-17.547, -17.465]

Parameterization:
x1: 1.7409470332773195e-16
x2: 0.9999999999999999", "Parameterization 15
b: -4.113 [-4.114, -4.111]
a: -2.68 [-2.716, -2.644]

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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": "2022-09-15T18:17:53.916524Z", "iopub.status.busy": "2022-09-15T18:17:53.915941Z", "iopub.status.idle": "2022-09-15T18:17:54.106358Z", "shell.execute_reply": "2022-09-15T18:17:54.105237Z" }, "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": "2022-09-15T18:17:54.111191Z", "iopub.status.busy": "2022-09-15T18:17:54.110841Z", "iopub.status.idle": "2022-09-15T18:18:09.545005Z", "shell.execute_reply": "2022-09-15T18:18:09.543973Z" }, "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: 2.369795709893773\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 6, HV: 24.876478282518654\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 7, HV: 24.876478282518654\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 8, HV: 24.876478282518654\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 9, HV: 24.876478282518654\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 10, HV: 36.541194930229054\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 11, HV: 36.541194930229054\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 12, HV: 36.541194930229054\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 13, HV: 36.541194930229054\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 14, HV: 36.541194930229054\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 15, HV: 36.541194930229054\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 16, HV: 41.461883884075164\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 17, HV: 41.461883884075164\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 18, HV: 43.97064011735803\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 19, HV: 43.97064011735803\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 20, HV: 43.97064011735803\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 21, HV: 43.97064011735803\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 22, HV: 49.5601363294096\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 23, HV: 49.5601363294096\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 49.5601363294096\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": 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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": "2022-09-15T18:18:21.936126Z", "iopub.status.busy": "2022-09-15T18:18:21.935790Z", "iopub.status.idle": "2022-09-15T18:18:24.023386Z", "shell.execute_reply": "2022-09-15T18:18:24.022158Z" }, "hidden_ranges": [], "originalKey": "c6296697-ef07-422d-b965-35e4e5104a12" }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Iteration')" ] }, "execution_count": 23, "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", "%matplotlib inline\n", "\n", "from matplotlib.cm import ScalarMappable\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([torch.zeros(N_INIT), torch.arange(1, N_BATCH+1).repeat(BATCH_SIZE, 1).t().reshape(-1)]).numpy()\n", "for i, train_obj in enumerate(outcomes_list):\n", " x = i\n", " sc = axes[x].scatter(train_obj[:n_results, 0], train_obj[:n_results,1], c=batch_number[:n_results], alpha=0.8)\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": "2022-09-15T18:18:24.028965Z", "iopub.status.busy": "2022-09-15T18:18:24.028492Z", "iopub.status.idle": "2022-09-15T18:18:24.273347Z", "shell.execute_reply": "2022-09-15T18:18:24.272256Z" }, "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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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\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_BATCH + 1]\n", "log_hv_difference_parego = np.log10(branin_currin.max_hv - np.asarray(parego_hv_list))[:N_BATCH + 1]\n", "log_hv_difference_ehvi = np.log10(branin_currin.max_hv - np.asarray(ehvi_hv_list))[:N_BATCH + 1]\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(xlabel='number of observations (beyond initial points)', ylabel='Log Hypervolume Difference')\n", "ax.legend(loc=\"lower right\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "python3", "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": "3.8.13" } }, "nbformat": 4, "nbformat_minor": 2 }