{ "cells": [ { "cell_type": "markdown", "id": "f23d463f", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "95e7a97a-bf78-48d4-a0c1-c0e8dfc4fed9", "papermill": { "duration": 0.009263, "end_time": "2024-07-23T19:54:29.983535", "exception": false, "start_time": "2024-07-23T19:54:29.974272", "status": "completed" }, "showInput": true, "tags": [] }, "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, "id": "d6048efd", "metadata": { "code_folding": [], "customInput": null, "execution": { "iopub.execute_input": "2024-07-23T19:54:30.002412Z", "iopub.status.busy": "2024-07-23T19:54:30.001960Z", "iopub.status.idle": "2024-07-23T19:54:33.610729Z", "shell.execute_reply": "2024-07-23T19:54:33.609973Z" }, "hidden_ranges": [], "originalKey": "06bf2029-0ea4-40b4-aced-956f1411cb6e", "papermill": { "duration": 3.632948, "end_time": "2024-07-23T19:54:33.625260", "exception": false, "start_time": "2024-07-23T19:54:29.992312", "status": "completed" }, "showInput": true, "tags": [] }, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:33] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:33] ax.utils.notebook.plotting: Please see\n", " (https://ax.dev/tutorials/visualizations.html#Fix-for-plots-that-are-not-rendering)\n", " if visualizations are not rendering.\n" ] }, { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import torch\n", "from ax.plot.pareto_frontier import plot_pareto_frontier\n", "from ax.plot.pareto_utils import compute_posterior_pareto_frontier\n", "from ax.service.ax_client import AxClient\n", "from ax.service.utils.instantiation import ObjectiveProperties\n", "\n", "# Plotting imports and initialization\n", "from ax.utils.notebook.plotting import init_notebook_plotting, render\n", "from botorch.test_functions.multi_objective import BraninCurrin\n", "\n", "init_notebook_plotting()" ] }, { "cell_type": "code", "execution_count": 2, "id": "5caad1f0", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:54:33.702958Z", "iopub.status.busy": "2024-07-23T19:54:33.702470Z", "iopub.status.idle": "2024-07-23T19:54:33.706715Z", "shell.execute_reply": "2024-07-23T19:54:33.706165Z" }, "papermill": { "duration": 0.044777, "end_time": "2024-07-23T19:54:33.708009", "exception": false, "start_time": "2024-07-23T19:54:33.663232", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "# Load our sample 2-objective problem\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": 3, "id": "247c5843", "metadata": { "code_folding": [], "customInput": null, "execution": { "iopub.execute_input": "2024-07-23T19:54:33.788697Z", "iopub.status.busy": "2024-07-23T19:54:33.788185Z", "iopub.status.idle": "2024-07-23T19:54:33.801902Z", "shell.execute_reply": "2024-07-23T19:54:33.801233Z" }, "executionStartTime": 1628191188673, "executionStopTime": 1628191188746, "hidden_ranges": [], "originalKey": "c687973d-1b09-4a8f-9108-1f74adf64d4d", "papermill": { "duration": 0.057077, "end_time": "2024-07-23T19:54:33.803491", "exception": false, "start_time": "2024-07-23T19:54:33.746414", "status": "completed" }, "requestMsgId": "ea523260-8896-48e4-a62f-3530d268b209", "showInput": true, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:33] 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 07-23 19:54:33] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:33] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:33] 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 07-23 19:54:33] 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 07-23 19:54:33] ax.modelbridge.dispatch_utils: Using Models.BOTORCH_MODULAR since there is at least one ordered parameter and there are no unordered categorical parameters.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:33] 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 07-23 19:54:33] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=5\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:33] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=5\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:33] ax.modelbridge.dispatch_utils: `verbose`, `disable_progbar`, and `jit_compile` are not yet supported when using `choose_generation_strategy` with ModularBoTorchModel, dropping these arguments.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:33] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+BoTorch', steps=[Sobol for 5 trials, BoTorch 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", "id": "4426adbb", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "70fd45e1-a2ce-4034-bb44-086507833472", "papermill": { "duration": 0.039056, "end_time": "2024-07-23T19:54:33.881615", "exception": false, "start_time": "2024-07-23T19:54:33.842559", "status": "completed" }, "showInput": true, "tags": [] }, "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": 4, "id": "b174e1ab", "metadata": { "code_folding": [], "customInput": null, "execution": { "iopub.execute_input": "2024-07-23T19:54:33.961671Z", "iopub.status.busy": "2024-07-23T19:54:33.961094Z", "iopub.status.idle": "2024-07-23T19:54:33.965177Z", "shell.execute_reply": "2024-07-23T19:54:33.964609Z" }, "executionStartTime": 1628191201840, "executionStopTime": 1628191201871, "hidden_ranges": [], "originalKey": "a0e4fa8d-ebc7-4dc6-b370-ed4a83e3208f", "papermill": { "duration": 0.045651, "end_time": "2024-07-23T19:54:33.966417", "exception": false, "start_time": "2024-07-23T19:54:33.920766", "status": "completed" }, "requestMsgId": "9cfd336d-c317-4d1c-a028-42d45903bac6", "showInput": true, "tags": [] }, "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", "id": "09ac0857", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "4200cd7c-8e13-4cbf-b0c1-72b52d900aaf", "papermill": { "duration": 0.038783, "end_time": "2024-07-23T19:54:34.044323", "exception": false, "start_time": "2024-07-23T19:54:34.005540", "status": "completed" }, "showInput": true, "tags": [] }, "source": [ "### Run Optimization" ] }, { "cell_type": "code", "execution_count": 5, "id": "70a54cb9", "metadata": { "customInput": null, "execution": { "iopub.execute_input": "2024-07-23T19:54:34.123376Z", "iopub.status.busy": "2024-07-23T19:54:34.122874Z", "iopub.status.idle": "2024-07-23T19:55:20.068995Z", "shell.execute_reply": "2024-07-23T19:55:20.068410Z" }, "executionStartTime": 1628191208271, "executionStopTime": 1628191238749, "originalKey": "f91b1a1e-c78a-4262-a211-a13115c007c1", "papermill": { "duration": 45.987263, "end_time": "2024-07-23T19:55:20.070430", "exception": false, "start_time": "2024-07-23T19:54:34.083167", "status": "completed" }, "requestMsgId": "842a1cf8-97a3-43d6-83a3-f258ea96ae20", "showInput": true, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:54:34] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.915697, 'x2': 0.299481} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:34] ax.service.ax_client: Completed trial 0 with data: {'a': (-9.028192, 0.0), 'b': (-8.33193, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:54:34] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.580851, 'x2': 0.149961} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:34] ax.service.ax_client: Completed trial 1 with data: {'a': (-2.064706, 0.0), 'b': (-10.83757, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:54:34] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.838598, 'x2': 0.164636} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:34] ax.service.ax_client: Completed trial 2 with data: {'a': (-13.842742, 0.0), 'b': (-9.887474, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:54:34] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.716842, 'x2': 0.932837} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:34] ax.service.ax_client: Completed trial 3 with data: {'a': (-183.998077, 0.0), 'b': (-4.43332, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:54:34] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.883702, 'x2': 0.440028} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:34] ax.service.ax_client: Completed trial 4 with data: {'a': (-30.602318, 0.0), 'b': (-7.000249, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:34] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.0, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:34] ax.service.ax_client: Completed trial 5 with data: {'a': (-17.508297, 0.0), 'b': (-1.180408, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.14/x64/lib/python3.10/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\n", "\n", "A not p.d., added jitter of 1.0e-08 to the diagonal\n", "\n", "[INFO 07-23 19:54:35] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.0, 'x2': 0.808202} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:35] ax.service.ax_client: Completed trial 6 with data: {'a': (-38.371155, 0.0), 'b': (-1.383998, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:36] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.151649, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:36] ax.service.ax_client: Completed trial 7 with data: {'a': (-14.931427, 0.0), 'b': (-5.200738, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:37] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.0, 'x2': 0.178435} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:37] ax.service.ax_client: Completed trial 8 with data: {'a': (-223.288132, 0.0), 'b': (-2.81796, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:38] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.062442, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:38] ax.service.ax_client: Completed trial 9 with data: {'a': (-4.356442, 0.0), 'b': (-3.516149, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:39] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.028274, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:40] ax.service.ax_client: Completed trial 10 with data: {'a': (-9.668906, 0.0), 'b': (-2.315367, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:41] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 1.0, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:41] ax.service.ax_client: Completed trial 11 with data: {'a': (-145.872208, 0.0), 'b': (-4.005316, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:42] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.0673, 'x2': 0.937939} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:42] ax.service.ax_client: Completed trial 12 with data: {'a': (-3.769835, 0.0), 'b': (-3.847423, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:46] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.076933, 'x2': 0.963646} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:46] ax.service.ax_client: Completed trial 13 with data: {'a': (-2.861984, 0.0), 'b': (-4.049937, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:48] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.013615, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:48] ax.service.ax_client: Completed trial 14 with data: {'a': (-13.372099, 0.0), 'b': (-1.735031, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:51] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.042489, 'x2': 0.98635} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:51] ax.service.ax_client: Completed trial 15 with data: {'a': (-7.078302, 0.0), 'b': (-2.876585, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:53] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.095148, 'x2': 0.912659} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:53] ax.service.ax_client: Completed trial 16 with data: {'a': (-1.402514, 0.0), 'b': (-4.695683, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:56] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.42263, 'x2': 0.799052} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:56] ax.service.ax_client: Completed trial 17 with data: {'a': (-74.387772, 0.0), 'b': (-5.717248, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:58] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.050799, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:54:58] ax.service.ax_client: Completed trial 18 with data: {'a': (-5.61823, 0.0), 'b': (-3.137197, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:02] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.006678, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:02] ax.service.ax_client: Completed trial 19 with data: {'a': (-15.398723, 0.0), 'b': (-1.45336, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:05] ax.service.ax_client: Generated new trial 20 with parameters {'x1': 0.111035, 'x2': 0.859094} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:05] ax.service.ax_client: Completed trial 20 with data: {'a': (-0.596418, 0.0), 'b': (-5.260275, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:08] ax.service.ax_client: Generated new trial 21 with parameters {'x1': 0.020711, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:08] ax.service.ax_client: Completed trial 21 with data: {'a': (-11.479138, 0.0), 'b': (-2.019151, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:11] ax.service.ax_client: Generated new trial 22 with parameters {'x1': 0.035465, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:11] ax.service.ax_client: Completed trial 22 with data: {'a': (-8.153015, 0.0), 'b': (-2.588728, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:15] ax.service.ax_client: Generated new trial 23 with parameters {'x1': 0.084317, 'x2': 0.931818} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:15] ax.service.ax_client: Completed trial 23 with data: {'a': (-2.093678, 0.0), 'b': (-4.35646, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:20] ax.service.ax_client: Generated new trial 24 with parameters {'x1': 0.00331, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:55:20] ax.service.ax_client: Completed trial 24 with data: {'a': (-16.443575, 0.0), 'b': (-1.315804, 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", "id": "5b74edfe", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "e0a6feb4-8c38-42e4-9d7c-62b79307e043", "papermill": { "duration": 0.04139, "end_time": 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"white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Pareto Frontier" }, "width": 750, "xaxis": { "ticksuffix": "", "title": { "text": "a" }, "zeroline": true }, "yaxis": { "ticksuffix": "", "title": { "text": "b" }, "zeroline": true } } }, "text/html": [ "
" ] }, "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", "id": "a4c24bb1", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "f4f6ce29-4a0c-4ac5-84a7-f83a4de9112c", "papermill": { "duration": 0.044642, "end_time": "2024-07-23T19:55:37.510786", "exception": false, "start_time": "2024-07-23T19:55:37.466144", "status": "completed" }, "showInput": true, "tags": [] }, "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", "id": "7ac3b242", "metadata": { "originalKey": "e04a24fa-dcfc-4430-960f-9c0e772fd754", "papermill": { "duration": 0.044533, "end_time": "2024-07-23T19:55:37.600007", "exception": false, "start_time": "2024-07-23T19:55:37.555474", "status": "completed" }, "showInput": true, "tags": [] }, "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", "id": "0c432c57", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "1842c5bf-4113-406b-b2c7-bc2535e9dd6c", "papermill": { "duration": 0.044412, "end_time": "2024-07-23T19:55:37.689178", "exception": false, "start_time": "2024-07-23T19:55:37.644766", "status": "completed" }, "showInput": false, "tags": [] }, "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", "id": "ca2d9e7d", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "cefa89be-ef41-40d9-9458-d6faed3c6c91", "papermill": { "duration": 0.04468, "end_time": "2024-07-23T19:55:37.778381", "exception": false, "start_time": "2024-07-23T19:55:37.733701", "status": "completed" }, "showInput": false, "tags": [] }, "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", "id": "02f69d25", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "1819970e-9b48-4b57-b280-35bf2c4919d2", "papermill": { "duration": 0.044891, "end_time": "2024-07-23T19:55:37.868963", "exception": false, "start_time": "2024-07-23T19:55:37.824072", "status": "completed" }, "showInput": false, "tags": [] }, "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", "id": "b98db080", "metadata": { "originalKey": "f2f39a8f-279f-49a1-b645-d51caed24d9c", "papermill": { "duration": 0.045664, "end_time": "2024-07-23T19:55:37.959487", "exception": false, "start_time": "2024-07-23T19:55:37.913823", "status": "completed" }, "tags": [] }, "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", "id": "a0cd9a43", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "0ac396dd-8040-4f87-8abe-472127734aef", "papermill": { "duration": 0.044625, "end_time": "2024-07-23T19:55:38.049295", "exception": false, "start_time": "2024-07-23T19:55:38.004670", "status": "completed" }, "tags": [] }, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 7, "id": "b7965c2d", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:38.139400Z", "iopub.status.busy": "2024-07-23T19:55:38.139121Z", "iopub.status.idle": "2024-07-23T19:55:38.143995Z", "shell.execute_reply": "2024-07-23T19:55:38.143427Z" }, "executionStartTime": 1628191302514, "executionStopTime": 1628191302546, "hidden_ranges": [], "originalKey": "500597fc-a996-48f4-a8fe-defd429162b8", "papermill": { "duration": 0.051701, "end_time": "2024-07-23T19:55:38.145322", "exception": false, "start_time": "2024-07-23T19:55:38.093621", "status": "completed" }, "requestMsgId": "07dd11c9-cd20-4bfa-b2d9-9a7bf70b2e44", "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from ax.core.data import Data\n", "from ax.core.experiment import Experiment\n", "from ax.core.metric import Metric\n", "from ax.core.objective import MultiObjective, Objective\n", "from ax.core.optimization_config import (\n", " MultiObjectiveOptimizationConfig,\n", " ObjectiveThreshold,\n", ")\n", "\n", "from ax.core.parameter import ParameterType, RangeParameter\n", "from ax.core.search_space import SearchSpace\n", "from ax.metrics.noisy_function import NoisyFunctionMetric\n", "\n", "# Analysis utilities, including a method to evaluate hypervolumes\n", "from ax.modelbridge.modelbridge_utils import observed_hypervolume\n", "from ax.modelbridge.registry import Models\n", "from ax.runners.synthetic import SyntheticRunner\n", "from ax.service.utils.report_utils import exp_to_df\n", "\n", "# BoTorch acquisition class for ParEGO\n", "from botorch.acquisition.multi_objective.parego import qLogNParEGO" ] }, { "cell_type": "markdown", "id": "1eb90c21", "metadata": { "originalKey": "0b43c263-41da-4aa8-99f3-4a2a7fc49e4b", "papermill": { "duration": 0.083135, "end_time": "2024-07-23T19:55:38.273003", "exception": false, "start_time": "2024-07-23T19:55:38.189868", "status": "completed" }, "tags": [] }, "source": [ "## Define experiment configurations" ] }, { "cell_type": "markdown", "id": "2df0b5d7", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "963a036d-a250-4e3c-9570-afe6f2192f9a", "papermill": { "duration": 0.044266, "end_time": "2024-07-23T19:55:38.361969", "exception": false, "start_time": "2024-07-23T19:55:38.317703", "status": "completed" }, "tags": [] }, "source": [ "### Search Space" ] }, { "cell_type": "code", "execution_count": 8, "id": "77888e02", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:38.452642Z", "iopub.status.busy": "2024-07-23T19:55:38.452088Z", "iopub.status.idle": "2024-07-23T19:55:38.455935Z", "shell.execute_reply": "2024-07-23T19:55:38.455351Z" }, "executionStartTime": 1628191313915, "executionStopTime": 1628191313944, "hidden_ranges": [], "originalKey": "90637eb4-730f-4f3d-8712-875bf88d6c2d", "papermill": { "duration": 0.050675, "end_time": "2024-07-23T19:55:38.457255", "exception": false, "start_time": "2024-07-23T19:55:38.406580", "status": "completed" }, "requestMsgId": "fbb9db8e-5414-4add-ad10-0bd00583ebf5", "tags": [] }, "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(parameters=[x1, x2])" ] }, { "cell_type": "markdown", "id": "6450bc76", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ac3cf1fe-d39d-48bb-a31d-e3ee0d70418b", "papermill": { "duration": 0.044347, "end_time": "2024-07-23T19:55:38.546169", "exception": false, "start_time": "2024-07-23T19:55:38.501822", "status": "completed" }, "showInput": false, "tags": [] }, "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": 9, "id": "dd6df7c6", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:38.636612Z", "iopub.status.busy": "2024-07-23T19:55:38.636076Z", "iopub.status.idle": "2024-07-23T19:55:38.640723Z", "shell.execute_reply": "2024-07-23T19:55:38.640120Z" }, "executionStartTime": 1628191319191, "executionStopTime": 1628191319220, "hidden_ranges": [], "originalKey": "9fdb11b6-7845-4f06-90fd-527fee088d76", "papermill": { "duration": 0.051406, "end_time": "2024-07-23T19:55:38.642032", "exception": false, "start_time": "2024-07-23T19:55:38.590626", "status": "completed" }, "requestMsgId": "febe0d60-fe60-4d55-ba6f-724c8ce7601d", "tags": [] }, "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": 10, "id": "b84f6cf5", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:38.732638Z", "iopub.status.busy": "2024-07-23T19:55:38.732131Z", "iopub.status.idle": "2024-07-23T19:55:38.735539Z", "shell.execute_reply": "2024-07-23T19:55:38.734918Z" }, "executionStartTime": 1628191321755, "executionStopTime": 1628191321791, "hidden_ranges": [], "originalKey": "27065b03-7234-49c1-b3ae-f6442ec4e3d6", "papermill": { "duration": 0.050346, "end_time": "2024-07-23T19:55:38.736870", "exception": false, "start_time": "2024-07-23T19:55:38.686524", "status": "completed" }, "requestMsgId": "d4010fca-5cbd-4a41-a779-cfa97ec15cc3", "tags": [] }, "outputs": [], "source": [ "mo = MultiObjective(\n", " objectives=[Objective(metric=metric_a), Objective(metric=metric_b)],\n", ")" ] }, { "cell_type": "code", "execution_count": 11, "id": "ecfb63cc", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:55:38.827638Z", "iopub.status.busy": "2024-07-23T19:55:38.827155Z", "iopub.status.idle": "2024-07-23T19:55:38.831051Z", "shell.execute_reply": "2024-07-23T19:55:38.830464Z" }, "executionStartTime": 1628191323464, "executionStopTime": 1628191323491, "originalKey": "c58b70de-06b5-4e03-8958-c3c55d4c295a", "papermill": { "duration": 0.050933, "end_time": "2024-07-23T19:55:38.832454", "exception": false, "start_time": "2024-07-23T19:55:38.781521", "status": "completed" }, "requestMsgId": "27e7efe5-d29e-4211-944e-41e6de065299", "tags": [] }, "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": 12, "id": "afa987b5", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:38.923393Z", "iopub.status.busy": "2024-07-23T19:55:38.922928Z", "iopub.status.idle": "2024-07-23T19:55:38.926234Z", "shell.execute_reply": "2024-07-23T19:55:38.925622Z" }, "executionStartTime": 1628191325491, "executionStopTime": 1628191325519, "hidden_ranges": [], "originalKey": "4b1ce9ba-e2e5-4a8a-9c15-5d01a2940a55", "papermill": { "duration": 0.050117, "end_time": "2024-07-23T19:55:38.927523", "exception": false, "start_time": "2024-07-23T19:55:38.877406", "status": "completed" }, "requestMsgId": "314ea591-0d2e-4fb5-b091-2aa2ea27f0eb", "tags": [] }, "outputs": [], "source": [ "optimization_config = MultiObjectiveOptimizationConfig(\n", " objective=mo,\n", " objective_thresholds=objective_thresholds,\n", ")" ] }, { "cell_type": "markdown", "id": "dc586ab5", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "3b7b797c-2478-48d6-84ea-c62a886db31f", "papermill": { "duration": 0.044941, "end_time": "2024-07-23T19:55:39.023807", "exception": false, "start_time": "2024-07-23T19:55:38.978866", "status": "completed" }, "showInput": false, "tags": [] }, "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": 13, "id": "2358cbec", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:55:39.115099Z", "iopub.status.busy": "2024-07-23T19:55:39.114430Z", "iopub.status.idle": "2024-07-23T19:55:39.117714Z", "shell.execute_reply": "2024-07-23T19:55:39.117127Z" }, "executionStartTime": 1628191328765, "executionStopTime": 1628191328792, "originalKey": "a52ace6c-8144-446b-97d5-2f27879ca187", "papermill": { "duration": 0.05048, "end_time": "2024-07-23T19:55:39.118990", "exception": false, "start_time": "2024-07-23T19:55:39.068510", "status": "completed" }, "requestMsgId": "6a222fb5-231e-4476-86a6-c29ca5113332", "tags": [] }, "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": 14, "id": "fd31d332", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:39.209756Z", "iopub.status.busy": "2024-07-23T19:55:39.209257Z", "iopub.status.idle": "2024-07-23T19:55:39.212912Z", "shell.execute_reply": "2024-07-23T19:55:39.212340Z" }, "executionStartTime": 1628191330913, "executionStopTime": 1628191330991, "hidden_ranges": [], "originalKey": "9fd6ec68-4c53-4276-a98a-61431cdc05d5", "papermill": { "duration": 0.050484, "end_time": "2024-07-23T19:55:39.214173", "exception": false, "start_time": "2024-07-23T19:55:39.163689", "status": "completed" }, "requestMsgId": "8f659995-6b8f-4544-8392-03daaf8220b8", "tags": [] }, "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": 15, "id": "31a9754a", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:39.305300Z", "iopub.status.busy": "2024-07-23T19:55:39.304798Z", "iopub.status.idle": "2024-07-23T19:55:39.308667Z", "shell.execute_reply": "2024-07-23T19:55:39.308017Z" }, "executionStartTime": 1628191334273, "executionStopTime": 1628191334299, "hidden_ranges": [], "originalKey": "a8eef6a6-1d53-494a-907f-10ca35492a8c", "papermill": { "duration": 0.051034, "end_time": "2024-07-23T19:55:39.309932", "exception": false, "start_time": "2024-07-23T19:55:39.258898", "status": "completed" }, "requestMsgId": "b207dbd4-0a53-4efd-bbb9-9dee8835d60b", "tags": [] }, "outputs": [], "source": [ "## Initialize with Sobol samples\n", "def initialize_experiment(experiment):\n", " sobol = Models.SOBOL(search_space=experiment.search_space, seed=1234)\n", " for _ in range(N_INIT):\n", " experiment.new_trial(sobol.gen(1)).run()\n", " return experiment.fetch_data()" ] }, { "cell_type": "markdown", "id": "36c67453", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "0c918735-9fda-4c36-90b5-163443e66c72", "papermill": { "duration": 0.045555, "end_time": "2024-07-23T19:55:39.400455", "exception": false, "start_time": "2024-07-23T19:55:39.354900", "status": "completed" }, "showInput": false, "tags": [] }, "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": 16, "id": "bff726d8", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:39.491916Z", "iopub.status.busy": "2024-07-23T19:55:39.491441Z", "iopub.status.idle": "2024-07-23T19:55:39.553721Z", "shell.execute_reply": "2024-07-23T19:55:39.553130Z" }, "executionStartTime": 1628191356513, "executionStopTime": 1628191356896, "hidden_ranges": [], "originalKey": "5ee13832-804a-413f-a6bc-1f8f96a817d8", "papermill": { "duration": 0.109748, "end_time": "2024-07-23T19:55:39.555279", "exception": false, "start_time": "2024-07-23T19:55:39.445531", "status": "completed" }, "requestMsgId": "5b40f1e6-45b9-40e4-8569-9d459e98ca57", "tags": [] }, "outputs": [], "source": [ "sobol_experiment = build_experiment()\n", "sobol_data = initialize_experiment(sobol_experiment)" ] }, { "cell_type": "code", "execution_count": 17, "id": "ff4312bd", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:39.646769Z", "iopub.status.busy": "2024-07-23T19:55:39.646158Z", "iopub.status.idle": "2024-07-23T19:55:46.739958Z", "shell.execute_reply": "2024-07-23T19:55:46.739166Z" }, "executionStartTime": 1628191362562, "executionStopTime": 1628191408255, "hidden_ranges": [], "originalKey": "0c6a6d44-29db-43dd-982d-dc664d00b009", "papermill": { "duration": 7.141276, "end_time": "2024-07-23T19:55:46.741424", "exception": false, "start_time": "2024-07-23T19:55:39.600148", "status": "completed" }, "requestMsgId": "8aca7b5b-aab8-4a39-9a49-d7b1e0c714c5", "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/core/data.py:286: FutureWarning:\n", "\n", "The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. 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Not appending column.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/core/data.py:286: FutureWarning:\n", "\n", "The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n", "\n", "[WARNING 07-23 19:55:39] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 0, HV: 0.0\n", "Iteration: 1, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/core/data.py:286: FutureWarning:\n", "\n", "The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. 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Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 2, HV: 0.0\n", "Iteration: 3, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/core/data.py:286: FutureWarning:\n", "\n", "The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n", "\n", "[WARNING 07-23 19:55:40] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/core/data.py:286: FutureWarning:\n", "\n", "The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. 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In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n", "\n", "[WARNING 07-23 19:55:46] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 23, HV: 18.30601777472312\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:55:46] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 18.30601777472312\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 = Models.BOTORCH_MODULAR(\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", "id": "a3afe1e4", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "767a7e9b-8902-424e-bfc4-f7afdba47302", "papermill": { "duration": 0.047181, "end_time": "2024-07-23T19:55:46.836134", "exception": false, "start_time": "2024-07-23T19:55:46.788953", "status": "completed" }, "tags": [] }, "source": [ "## qNEHVI\n", "Noisy Expected Hypervolume Improvement. This is our current recommended algorithm for multi-objective optimization." ] }, { "cell_type": "code", "execution_count": 18, "id": "5e0a69bc", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:46.933083Z", "iopub.status.busy": "2024-07-23T19:55:46.932498Z", "iopub.status.idle": "2024-07-23T19:55:46.994590Z", "shell.execute_reply": "2024-07-23T19:55:46.993802Z" }, "executionStartTime": 1628191422463, "executionStopTime": 1628191422803, "hidden_ranges": [], "originalKey": "8fc6bfb4-3012-4ce2-99ed-288378098c50", "papermill": { "duration": 0.112963, "end_time": "2024-07-23T19:55:46.996381", "exception": false, "start_time": "2024-07-23T19:55:46.883418", "status": "completed" }, "requestMsgId": "0fd945a2-ac45-4a74-82cc-7173e15ced85", "tags": [] }, "outputs": [], "source": [ "ehvi_experiment = build_experiment()\n", "ehvi_data = initialize_experiment(ehvi_experiment)" ] }, { "cell_type": "code", "execution_count": 19, "id": "c82d536b", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:55:47.093170Z", "iopub.status.busy": "2024-07-23T19:55:47.092436Z", "iopub.status.idle": "2024-07-23T19:57:03.740698Z", "shell.execute_reply": "2024-07-23T19:57:03.739985Z" }, "executionStartTime": 1628191425090, "executionStopTime": 1628191500240, "hidden_ranges": [], "originalKey": "27dd9425-b77e-4027-8412-30dd40c5abf1", "papermill": { "duration": 76.698171, "end_time": "2024-07-23T19:57:03.742080", "exception": false, "start_time": "2024-07-23T19:55:47.043909", "status": "completed" }, "requestMsgId": "65430b82-de1e-4946-9d8d-4a75762354c1", "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:55:48] ax.service.utils.report_utils: Column reason missing for all trials. 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Not appending column.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:03] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 57.2045473745027\n" ] } ], "source": [ "ehvi_hv_list = []\n", "ehvi_model = None\n", "for i in range(N_BATCH):\n", " ehvi_model = Models.BOTORCH_MODULAR(\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", "id": "34752de4", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "e93178b6-5ba4-4c01-b8a2-e05971b7326f", "papermill": { "duration": 0.04894, "end_time": "2024-07-23T19:57:03.840626", "exception": false, "start_time": "2024-07-23T19:57:03.791686", "status": "completed" }, "showInput": false, "tags": [] }, "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": 20, "id": "e945d7ca", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:57:03.943158Z", "iopub.status.busy": "2024-07-23T19:57:03.942466Z", "iopub.status.idle": "2024-07-23T19:57:18.522339Z", "shell.execute_reply": "2024-07-23T19:57:18.521601Z" }, "executionStartTime": 1628191505148, "executionStopTime": 1628191521900, "hidden_ranges": [], "originalKey": "71e013c5-638f-4ba4-bb9a-3e4a7d3eb9fa", "papermill": { "duration": 14.633036, "end_time": "2024-07-23T19:57:18.523758", "exception": false, "start_time": "2024-07-23T19:57:03.890722", "status": "completed" }, "requestMsgId": "681433c5-fc21-4699-9fe1-8e444c671153", "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "error_x": { "array": [ 0.07760044234276738, 0.07760044234276738, 0.04717309086176064, 0.047430134368084936, 0.07760044219059226, 0.07760044229204234, 0.07760044244421746, 0.04670129857735696, 0.050408162840856335, 0.07760044234276738, 0.06302491053133925, 0.07760044244421746, 0.04709335801001863, 0.04584324609472079, 0.04699120564123501, 0.08469958994824166, 0.046849942617594106, 0.06884965125001254, 0.06453035113655393, 0.08210142212903425 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "error_y": { "array": [ 0.0037519346018938184, 0.0037519346018938184, 0.002337995208070945, 0.0023404567310704423, 0.0037519346018938184, 0.003751934599632531, 0.003751934606416393, 0.00236026362930989, 0.002414810722131889, 0.0037519346018938184, 0.002963721639111955, 0.003751934608677681, 0.0023514866131530616, 0.0023171526433138283, 0.002315041443855256, 0.00401084153348603, 0.0023630769661626043, 0.0034460706365355784, 0.002994428936874293, 0.003825610930787905 ], "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=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", "id": "7f54f00a", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "77b2dbce-f1e4-443a-8f81-2e1cbe207301", "papermill": { "duration": 0.053202, "end_time": "2024-07-23T19:57:18.630553", "exception": false, "start_time": "2024-07-23T19:57:18.577351", "status": "completed" }, "tags": [] }, "source": [ "## qNParEGO\n", "This is a good alternative algorithm for multi-objective optimization when qNEHVI runs too slowly. We use `qLogNParEGO` acquisition function with Modular BoTorch Model." ] }, { "cell_type": "code", "execution_count": 21, "id": "31252a93", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:57:18.739990Z", "iopub.status.busy": "2024-07-23T19:57:18.739467Z", "iopub.status.idle": "2024-07-23T19:57:18.802595Z", "shell.execute_reply": "2024-07-23T19:57:18.801786Z" }, "hidden_ranges": [], "originalKey": "2f796182-558b-47aa-8072-4dbf40123133", "papermill": { "duration": 0.119615, "end_time": "2024-07-23T19:57:18.804335", "exception": false, "start_time": "2024-07-23T19:57:18.684720", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "parego_experiment = build_experiment()\n", "parego_data = initialize_experiment(parego_experiment)" ] }, { "cell_type": "code", "execution_count": 22, "id": "14da196e", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:57:18.919823Z", "iopub.status.busy": "2024-07-23T19:57:18.919296Z", "iopub.status.idle": "2024-07-23T19:58:03.625362Z", "shell.execute_reply": "2024-07-23T19:58:03.624668Z" }, "hidden_ranges": [], "originalKey": "72999188-90f5-43e0-b1d9-d468e7d51191", "papermill": { "duration": 44.769249, "end_time": "2024-07-23T19:58:03.626797", "exception": false, "start_time": "2024-07-23T19:57:18.857548", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:19] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 0, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:21] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 1, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:23] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 2, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:24] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 3, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:25] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 4, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:26] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 5, HV: 14.613575245427366\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.14/x64/lib/python3.10/site-packages/botorch/optim/optimize.py:564: RuntimeWarning:\n", "\n", "Optimization failed in `gen_candidates_scipy` with the following warning(s):\n", "[NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal'), OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 2 and message ABNORMAL_TERMINATION_IN_LNSRCH.'), NumericalWarning('A not p.d., added jitter of 1.0e-08 to the diagonal')]\n", "Trying again with a new set of initial conditions.\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:31] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 6, HV: 16.427585602641685\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:33] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 7, HV: 16.427585602641685\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:34] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 8, HV: 32.14237425834501\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:36] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 9, HV: 33.110771019463286\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:37] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 10, HV: 42.98338020164138\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:40] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 11, HV: 42.98338020164138\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.14/x64/lib/python3.10/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\n", "\n", "A not p.d., added jitter of 1.0e-08 to the diagonal\n", "\n", "[WARNING 07-23 19:57:40] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 12, HV: 43.88744780746382\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:42] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 13, HV: 43.88744780746382\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.14/x64/lib/python3.10/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning:\n", "\n", "A not p.d., added jitter of 1.0e-08 to the diagonal\n", "\n", "[WARNING 07-23 19:57:42] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 14, HV: 44.02985957566082\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:44] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 15, HV: 44.02985957566082\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:46] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 16, HV: 48.14813378805327\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:47] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 17, HV: 48.56230462281859\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:48] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 18, HV: 48.57507649079132\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.14/x64/lib/python3.10/site-packages/botorch/optim/optimize.py:564: RuntimeWarning:\n", "\n", "Optimization failed in `gen_candidates_scipy` with the following warning(s):\n", "[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 2 and message ABNORMAL_TERMINATION_IN_LNSRCH.')]\n", "Trying again with a new set of initial conditions.\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:51] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 19, HV: 48.802627484317\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:53] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 20, HV: 48.815767764152255\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:57:55] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 21, HV: 48.85623491086302\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.14/x64/lib/python3.10/site-packages/botorch/optim/optimize.py:564: RuntimeWarning:\n", "\n", "Optimization failed in `gen_candidates_scipy` with the following warning(s):\n", "[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 2 and message ABNORMAL_TERMINATION_IN_LNSRCH.'), OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 2 and message ABNORMAL_TERMINATION_IN_LNSRCH.')]\n", "Trying again with a new set of initial conditions.\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.14/x64/lib/python3.10/site-packages/botorch/optim/optimize.py:564: RuntimeWarning:\n", "\n", "Optimization failed on the second try, after generating a new set of initial conditions.\n", "\n", "[WARNING 07-23 19:57:58] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 22, HV: 48.925845972280925\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:58:00] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 23, HV: 48.92717422983995\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.14/x64/lib/python3.10/site-packages/botorch/optim/optimize.py:564: RuntimeWarning:\n", "\n", "Optimization failed in `gen_candidates_scipy` with the following warning(s):\n", "[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 2 and message ABNORMAL_TERMINATION_IN_LNSRCH.')]\n", "Trying again with a new set of initial conditions.\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:58:03] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 07-23 19:58:03] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 48.92857642091531\n" ] } ], "source": [ "parego_hv_list = []\n", "parego_model = None\n", "for i in range(N_BATCH):\n", " parego_model = Models.BOTORCH_MODULAR(\n", " experiment=parego_experiment,\n", " data=parego_data,\n", " botorch_acqf_class=qLogNParEGO,\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", "id": "a919c745", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "67ded85f-7c58-4c31-8df5-b0d8d07e4299", "papermill": { "duration": 0.055099, "end_time": "2024-07-23T19:58:03.738032", "exception": false, "start_time": "2024-07-23T19:58:03.682933", "status": "completed" }, "showInput": false, "tags": [] }, "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": 23, "id": "6d18885a", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:58:03.851003Z", "iopub.status.busy": "2024-07-23T19:58:03.850497Z", "iopub.status.idle": "2024-07-23T19:58:23.801889Z", "shell.execute_reply": "2024-07-23T19:58:23.801164Z" }, "hidden_ranges": [], "originalKey": "3b1f39fd-ef75-4ea4-865b-f7b54b90da07", "papermill": { "duration": 20.009528, "end_time": "2024-07-23T19:58:23.803169", "exception": false, "start_time": "2024-07-23T19:58:03.793641", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "error_x": { "array": [ 0.017302694186258016, 0.031115040394139242, 0.022801209470158405, 0.01941931083813346, 0.020175644367829388, 0.023419276873397343, 0.03410662912221561, 0.03262925500900705, 0.031069068397907657, 0.015390772433890327, 0.014960560005895431, 0.017621808721862257, 0.015032971376242642, 0.021092099447766428, 0.014978522495612701, 0.03319928100001045, 0.033012746210822064, 0.48154715726996433, 0.015796426833757655, 0.033476718873863644 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "error_y": { "array": [ 0.001961645435498438, 0.0029287888010496523, 0.0023333067600136677, 0.0020888882511421883, 0.002146317014612219, 0.002593082263235344, 0.003380678981252535, 0.0030545249305098288, 0.002925143293746192, 0.0016779657636873924, 0.0015791469346228895, 0.0019375199971202908, 0.0015906335626553983, 0.0022131854051009358, 0.0015862833275463585, 0.0031060346380092658, 0.003441842075556574, 0.026301816106792313, 0.001728721248323582, 0.003390058930427654 ], "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: -16.941 [-16.958, -16.924]
b: -1.252 [-1.254, -1.250]

Parameterization:
x1: 0.001748950074694648
x2: 1.0", "Parameterization 1
a: -12.045 [-12.076, -12.014]
b: -1.931 [-1.934, -1.928]

Parameterization:
x1: 0.018507210129876366
x2: 1.0", "Parameterization 2
a: -13.506 [-13.529, -13.483]
b: -1.716 [-1.718, -1.713]

Parameterization:
x1: 0.013135601295906914
x2: 0.9999999999999998", "Parameterization 3
a: -14.094 [-14.114, -14.075]
b: -1.632 [-1.634, -1.630]

Parameterization:
x1: 0.011074147943851698
x2: 1.0", "Parameterization 4
a: -13.953 [-13.973, -13.933]
b: -1.652 [-1.654, -1.650]

Parameterization:
x1: 0.011563638253404035
x2: 1.0", "Parameterization 5
a: -17.506 [-17.530, -17.483]
b: -1.18 [-1.183, -1.178]

Parameterization:
x1: 0.0
x2: 0.9999999999999987", "Parameterization 6
a: -6.595 [-6.630, -6.561]
b: -2.907 [-2.910, -2.903]

Parameterization:
x1: 0.04417998568020651
x2: 1.0", "Parameterization 7
a: -11.684 [-11.717, -11.651]
b: -1.987 [-1.990, -1.984]

Parameterization:
x1: 0.019899837186092163
x2: 1.0", "Parameterization 8
a: -12.055 [-12.086, -12.024]
b: -1.93 [-1.933, -1.927]

Parameterization:
x1: 0.018469278459116036
x2: 0.9999999999999999", "Parameterization 9
a: -16.48 [-16.496, -16.465]
b: -1.311 [-1.313, -1.310]

Parameterization:
x1: 0.0031974493415954934
x2: 0.9999999999999999", "Parameterization 10
a: -15.992 [-16.007, -15.977]
b: -1.375 [-1.377, -1.373]

Parameterization:
x1: 0.0047545490872054974
x2: 1.0", "Parameterization 11
a: -14.482 [-14.499, -14.464]
b: -1.578 [-1.580, -1.576]

Parameterization:
x1: 0.009745550430159653
x2: 1.0", "Parameterization 12
a: -15.728 [-15.743, -15.713]
b: -1.41 [-1.411, -1.408]

Parameterization:
x1: 0.005606167442013387
x2: 1.0", "Parameterization 13
a: -13.792 [-13.813, -13.770]
b: -1.675 [-1.677, -1.673]

Parameterization:
x1: 0.01212808276916791
x2: 0.9999999999999999", "Parameterization 14
a: -16.103 [-16.118, -16.088]
b: -1.36 [-1.362, -1.359]

Parameterization:
x1: 0.004397950864049686
x2: 1.0", "Parameterization 15
a: -11.522 [-11.555, -11.489]
b: -2.012 [-2.015, -2.009]

Parameterization:
x1: 0.020532375457470647
x2: 1.0", "Parameterization 16
a: -8.339 [-8.372, -8.306]
b: -2.553 [-2.557, -2.550]

Parameterization:
x1: 0.03452521337627774
x2: 1.0", "Parameterization 17
a: -3.411 [-3.893, -2.929]
b: -3.992 [-4.018, -3.966]

Parameterization:
x1: 0.07867976080173021
x2: 1.0", "Parameterization 18
a: -15.093 [-15.108, -15.077]
b: -1.495 [-1.497, -1.493]

Parameterization:
x1: 0.007692793449083784
x2: 1.0", "Parameterization 19
a: -6.989 [-7.023, -6.956]
b: -2.821 [-2.825, -2.818]

Parameterization:
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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", "id": "e2ad29d0", "metadata": { "code_folding": [], "collapsed": true, "hidden_ranges": [], "jupyter": { "outputs_hidden": true }, "originalKey": "a67f7345-1777-4372-8704-bb80c4c4e783", "papermill": { "duration": 0.059433, "end_time": "2024-07-23T19:58:23.922374", "exception": false, "start_time": "2024-07-23T19:58:23.862941", "status": "completed" }, "tags": [] }, "source": [ "## Plot empirical data" ] }, { "cell_type": "markdown", "id": "042ae2cd", "metadata": { "code_folding": [], "collapsed": true, "hidden_ranges": [], "jupyter": { "outputs_hidden": true }, "originalKey": "de878adc-0eb2-4599-8c1b-e0adbc0c0765", "papermill": { "duration": 0.059236, "end_time": "2024-07-23T19:58:24.041503", "exception": false, "start_time": "2024-07-23T19:58:23.982267", "status": "completed" }, "showInput": false, "tags": [] }, "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": 24, "id": "db17c3b2", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:58:24.161752Z", "iopub.status.busy": "2024-07-23T19:58:24.161277Z", "iopub.status.idle": "2024-07-23T19:58:25.520807Z", "shell.execute_reply": "2024-07-23T19:58:25.520178Z" }, "hidden_ranges": [], "originalKey": "c6296697-ef07-422d-b965-35e4e5104a12", "papermill": { "duration": 1.421276, "end_time": "2024-07-23T19:58:25.522106", "exception": false, "start_time": "2024-07-23T19:58:24.100830", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Iteration')" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from matplotlib.cm import ScalarMappable\n", "\n", "%matplotlib inline\n", "\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 = matplotlib.colormaps[\"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", "id": "799ca5c6", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ca12287f-c7b8-4ef8-8eb9-57760eda5fed", "papermill": { "duration": 0.059482, "end_time": "2024-07-23T19:58:25.641732", "exception": false, "start_time": "2024-07-23T19:58:25.582250", "status": "completed" }, "showInput": true, "tags": [] }, "source": [ "# Hypervolume statistics\n", "The hypervolume of the space dominated by points that dominate the reference point." ] }, { "cell_type": "markdown", "id": "7c9a4c29", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ec8b764b-c27d-4722-9e3d-d81cebb3624a", "papermill": { "duration": 0.060785, "end_time": "2024-07-23T19:58:25.762314", "exception": false, "start_time": "2024-07-23T19:58:25.701529", "status": "completed" }, "tags": [] }, "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": 25, "id": "925c4b23", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-07-23T19:58:25.883762Z", "iopub.status.busy": "2024-07-23T19:58:25.883303Z", "iopub.status.idle": "2024-07-23T19:58:26.054687Z", "shell.execute_reply": "2024-07-23T19:58:26.053997Z" }, "hidden_ranges": [], "originalKey": "d50b98bc-5ab1-4826-a5b2-474a13f4bae0", "papermill": { "duration": 0.233151, "end_time": "2024-07-23T19:58:26.056037", "exception": false, "start_time": "2024-07-23T19:58:25.822886", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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\")" ] } ], "metadata": { "fileHeader": "", "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": "3.10.14" }, "papermill": { "default_parameters": {}, "duration": 239.065794, "end_time": "2024-07-23T19:58:28.433835", "environment_variables": {}, "exception": null, "input_path": "/tmp/tmp.DL1QmpHQMI/Ax-main/tutorials/multiobjective_optimization.ipynb", "output_path": "/tmp/tmp.DL1QmpHQMI/Ax-main/tutorials/multiobjective_optimization.ipynb", "parameters": {}, "start_time": "2024-07-23T19:54:29.368041", "version": "2.6.0" } }, "nbformat": 4, "nbformat_minor": 5 }