{ "cells": [ { "cell_type": "markdown", "id": "dd75f122", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "95e7a97a-bf78-48d4-a0c1-c0e8dfc4fed9", "papermill": { "duration": 0.009285, "end_time": "2024-04-27T05:34:58.091408", "exception": false, "start_time": "2024-04-27T05:34:58.082123", "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": "2f14521e", "metadata": { "code_folding": [], "customInput": null, "execution": { "iopub.execute_input": "2024-04-27T05:34:58.110074Z", "iopub.status.busy": "2024-04-27T05:34:58.109733Z", "iopub.status.idle": "2024-04-27T05:35:01.528967Z", "shell.execute_reply": "2024-04-27T05:35:01.527926Z" }, "hidden_ranges": [], "originalKey": "06bf2029-0ea4-40b4-aced-956f1411cb6e", "papermill": { "duration": 3.443005, "end_time": "2024-04-27T05:35:01.543174", "exception": false, "start_time": "2024-04-27T05:34:58.100169", "status": "completed" }, "showInput": true, "tags": [] }, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:01] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:01] 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": "77987d78", "metadata": { "execution": { "iopub.execute_input": "2024-04-27T05:35:01.624618Z", "iopub.status.busy": "2024-04-27T05:35:01.624148Z", "iopub.status.idle": "2024-04-27T05:35:01.628489Z", "shell.execute_reply": "2024-04-27T05:35:01.627972Z" }, "papermill": { "duration": 0.047095, "end_time": "2024-04-27T05:35:01.629821", "exception": false, "start_time": "2024-04-27T05:35:01.582726", "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": "2674add4", "metadata": { "code_folding": [], "customInput": null, "execution": { "iopub.execute_input": "2024-04-27T05:35:01.711673Z", "iopub.status.busy": "2024-04-27T05:35:01.711193Z", "iopub.status.idle": "2024-04-27T05:35:01.724146Z", "shell.execute_reply": "2024-04-27T05:35:01.723493Z" }, "executionStartTime": 1628191188673, "executionStopTime": 1628191188746, "hidden_ranges": [], "originalKey": "c687973d-1b09-4a8f-9108-1f74adf64d4d", "papermill": { "duration": 0.055554, "end_time": "2024-04-27T05:35:01.725448", "exception": false, "start_time": "2024-04-27T05:35:01.669894", "status": "completed" }, "requestMsgId": "ea523260-8896-48e4-a62f-3530d268b209", "showInput": true, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:01] 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 04-27 05:35:01] 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 04-27 05:35:01] 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 04-27 05:35:01] 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 04-27 05:35:01] 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 04-27 05:35:01] 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 04-27 05:35:01] 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 04-27 05:35:01] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=5\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:01] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=5\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:01] 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 04-27 05:35:01] 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": "b7a69f73", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "70fd45e1-a2ce-4034-bb44-086507833472", "papermill": { "duration": 0.040682, "end_time": "2024-04-27T05:35:01.807110", "exception": false, "start_time": "2024-04-27T05:35:01.766428", "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": "17e2bfa0", "metadata": { "code_folding": [], "customInput": null, "execution": { "iopub.execute_input": "2024-04-27T05:35:01.890052Z", "iopub.status.busy": "2024-04-27T05:35:01.889782Z", "iopub.status.idle": "2024-04-27T05:35:01.893820Z", "shell.execute_reply": "2024-04-27T05:35:01.893199Z" }, "executionStartTime": 1628191201840, "executionStopTime": 1628191201871, "hidden_ranges": [], "originalKey": "a0e4fa8d-ebc7-4dc6-b370-ed4a83e3208f", "papermill": { "duration": 0.047319, "end_time": "2024-04-27T05:35:01.895166", "exception": false, "start_time": "2024-04-27T05:35:01.847847", "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": "747eb4bc", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "4200cd7c-8e13-4cbf-b0c1-72b52d900aaf", "papermill": { "duration": 0.041023, "end_time": "2024-04-27T05:35:01.977094", "exception": false, "start_time": "2024-04-27T05:35:01.936071", "status": "completed" }, "showInput": true, "tags": [] }, "source": [ "### Run Optimization" ] }, { "cell_type": "code", "execution_count": 5, "id": "7ee33d51", "metadata": { "customInput": null, "execution": { "iopub.execute_input": "2024-04-27T05:35:02.060579Z", "iopub.status.busy": "2024-04-27T05:35:02.060074Z", "iopub.status.idle": "2024-04-27T05:35:44.069143Z", "shell.execute_reply": "2024-04-27T05:35:44.068471Z" }, "executionStartTime": 1628191208271, "executionStopTime": 1628191238749, "originalKey": "f91b1a1e-c78a-4262-a211-a13115c007c1", "papermill": { "duration": 42.052519, "end_time": "2024-04-27T05:35:44.070478", "exception": false, "start_time": "2024-04-27T05:35:02.017959", "status": "completed" }, "requestMsgId": "842a1cf8-97a3-43d6-83a3-f258ea96ae20", "showInput": true, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.055765, 'x2': 0.256874} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Completed trial 0 with data: {'a': (-126.27124, 0.0), 'b': (-7.196263, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.166228, 'x2': 0.13164} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Completed trial 1 with data: {'a': (-80.174973, 0.0), 'b': (-13.172913, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.682078, 'x2': 0.963139} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Completed trial 2 with data: {'a': (-189.994812, 0.0), 'b': (-4.374009, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.028653, 'x2': 0.059581} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Completed trial 3 with data: {'a': (-235.993362, 0.0), 'b': (-5.920244, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.305908, 'x2': 0.022225} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Completed trial 4 with data: {'a': (-59.037498, 0.0), 'b': (-13.313398, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.675325, 'x2': 0.24245} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:02] ax.service.ax_client: Completed trial 5 with data: {'a': (-19.66116, 0.0), 'b': (-9.448742, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:03] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 1.0, 'x2': 0.183519} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:03] ax.service.ax_client: Completed trial 6 with data: {'a': (-2.005727, 0.0), 'b': (-9.511936, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:04] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.0, 'x2': 0.853429} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:04] ax.service.ax_client: Completed trial 7 with data: {'a': (-31.960102, 0.0), 'b': (-1.330139, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:05] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.0, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:05] ax.service.ax_client: Completed trial 8 with data: {'a': (-17.508297, 0.0), 'b': (-1.180408, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:06] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.084573, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:06] ax.service.ax_client: Completed trial 9 with data: {'a': (-3.614368, 0.0), 'b': (-4.134211, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:08] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.042022, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:08] ax.service.ax_client: Completed trial 10 with data: {'a': (-6.950634, 0.0), 'b': (-2.829522, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:09] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.438534, 'x2': 0.613968} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:09] ax.service.ax_client: Completed trial 11 with data: {'a': (-39.083366, 0.0), 'b': (-6.776071, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:10] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.083608, 'x2': 0.908278} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:10] ax.service.ax_client: Completed trial 12 with data: {'a': (-2.120916, 0.0), 'b': (-4.42214, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:12] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.019316, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:12] ax.service.ax_client: Completed trial 13 with data: {'a': (-11.836764, 0.0), 'b': (-1.963683, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:15] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.009383, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:15] ax.service.ax_client: Completed trial 14 with data: {'a': (-14.58805, 0.0), 'b': (-1.563544, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:17] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 1.0, 'x2': 0.790897} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:17] ax.service.ax_client: Completed trial 15 with data: {'a': (-80.451439, 0.0), 'b': (-4.769857, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:20] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.106768, 'x2': 0.90042} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:20] ax.service.ax_client: Completed trial 16 with data: {'a': (-1.079498, 0.0), 'b': (-4.996861, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:21] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.058698, 'x2': 0.975858} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:21] ax.service.ax_client: Completed trial 17 with data: {'a': (-4.647222, 0.0), 'b': (-3.462553, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:24] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.050534, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:24] ax.service.ax_client: Completed trial 18 with data: {'a': (-5.653658, 0.0), 'b': (-3.128189, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:27] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.113774, 'x2': 0.838056} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:27] ax.service.ax_client: Completed trial 19 with data: {'a': (-0.513465, 0.0), 'b': (-5.410245, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:30] ax.service.ax_client: Generated new trial 20 with parameters {'x1': 0.071933, 'x2': 0.964664} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:30] ax.service.ax_client: Completed trial 20 with data: {'a': (-3.229003, 0.0), 'b': (-3.904418, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:33] ax.service.ax_client: Generated new trial 21 with parameters {'x1': 0.029989, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:33] ax.service.ax_client: Completed trial 21 with data: {'a': (-9.288929, 0.0), 'b': (-2.381368, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:37] ax.service.ax_client: Generated new trial 22 with parameters {'x1': 0.004631, 'x2': 1.0} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:37] ax.service.ax_client: Completed trial 22 with data: {'a': (-16.029118, 0.0), 'b': (-1.369791, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:39] ax.service.ax_client: Generated new trial 23 with parameters {'x1': 0.866478, 'x2': 0.438045} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:39] ax.service.ax_client: Completed trial 23 with data: {'a': (-33.997074, 0.0), 'b': (-7.035689, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:44] ax.service.ax_client: Generated new trial 24 with parameters {'x1': 0.065481, 'x2': 0.981885} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-27 05:35:44] ax.service.ax_client: Completed trial 24 with data: {'a': (-3.915551, 0.0), 'b': (-3.66026, 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": "61ebdcb5", "metadata": { "code_folding": [], "customInput": null, "hidden_ranges": [], "originalKey": "e0a6feb4-8c38-42e4-9d7c-62b79307e043", "papermill": { "duration": 0.043114, "end_time": "2024-04-27T05:35:44.156442", "exception": false, "start_time": "2024-04-27T05:35:44.113328", "status": "completed" }, "showInput": false, "tags": [] }, "source": [ "### Plot Pareto Frontier" ] }, { "cell_type": "code", "execution_count": 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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", "id": "1cfabdb3", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "f4f6ce29-4a0c-4ac5-84a7-f83a4de9112c", "papermill": { "duration": 0.046447, "end_time": "2024-04-27T05:36:00.865675", "exception": false, "start_time": "2024-04-27T05:36:00.819228", "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": "17febfad", "metadata": { "originalKey": "e04a24fa-dcfc-4430-960f-9c0e772fd754", "papermill": { "duration": 0.046653, "end_time": "2024-04-27T05:36:00.958899", "exception": false, "start_time": "2024-04-27T05:36:00.912246", "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": "7a29e592", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "1842c5bf-4113-406b-b2c7-bc2535e9dd6c", "papermill": { "duration": 0.046465, "end_time": "2024-04-27T05:36:01.052287", "exception": false, "start_time": "2024-04-27T05:36:01.005822", "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": "5963ba36", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "cefa89be-ef41-40d9-9458-d6faed3c6c91", "papermill": { "duration": 0.046893, "end_time": "2024-04-27T05:36:01.145600", "exception": false, "start_time": "2024-04-27T05:36:01.098707", "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": "921b7768", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "1819970e-9b48-4b57-b280-35bf2c4919d2", "papermill": { "duration": 0.046341, "end_time": "2024-04-27T05:36:01.238720", "exception": false, "start_time": "2024-04-27T05:36:01.192379", "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": "ee55745b", "metadata": { "originalKey": "f2f39a8f-279f-49a1-b645-d51caed24d9c", "papermill": { "duration": 0.046943, "end_time": "2024-04-27T05:36:01.332337", "exception": false, "start_time": "2024-04-27T05:36:01.285394", "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": "eff8d71d", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "0ac396dd-8040-4f87-8abe-472127734aef", "papermill": { "duration": 0.046756, "end_time": "2024-04-27T05:36:01.425440", "exception": false, "start_time": "2024-04-27T05:36:01.378684", "status": "completed" }, "tags": [] }, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 7, "id": "a4ab6417", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:01.520394Z", "iopub.status.busy": "2024-04-27T05:36:01.520101Z", "iopub.status.idle": "2024-04-27T05:36:01.525191Z", "shell.execute_reply": "2024-04-27T05:36:01.524642Z" }, "executionStartTime": 1628191302514, "executionStopTime": 1628191302546, "hidden_ranges": [], "originalKey": "500597fc-a996-48f4-a8fe-defd429162b8", "papermill": { "duration": 0.054082, "end_time": "2024-04-27T05:36:01.526461", "exception": false, "start_time": "2024-04-27T05:36:01.472379", "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", "# 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\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" ] }, { "cell_type": "markdown", "id": "9b70d77a", "metadata": { "originalKey": "0b43c263-41da-4aa8-99f3-4a2a7fc49e4b", "papermill": { "duration": 0.046858, "end_time": "2024-04-27T05:36:01.619807", "exception": false, "start_time": "2024-04-27T05:36:01.572949", "status": "completed" }, "tags": [] }, "source": [ "## Define experiment configurations" ] }, { "cell_type": "markdown", "id": "eb838c7a", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "963a036d-a250-4e3c-9570-afe6f2192f9a", "papermill": { "duration": 0.046785, "end_time": "2024-04-27T05:36:01.713416", "exception": false, "start_time": "2024-04-27T05:36:01.666631", "status": "completed" }, "tags": [] }, "source": [ "### Search Space" ] }, { "cell_type": "code", "execution_count": 8, "id": "d0ed2c6c", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:01.808896Z", "iopub.status.busy": "2024-04-27T05:36:01.808347Z", "iopub.status.idle": "2024-04-27T05:36:01.812367Z", "shell.execute_reply": "2024-04-27T05:36:01.811702Z" }, "executionStartTime": 1628191313915, "executionStopTime": 1628191313944, "hidden_ranges": [], "originalKey": "90637eb4-730f-4f3d-8712-875bf88d6c2d", "papermill": { "duration": 0.053336, "end_time": "2024-04-27T05:36:01.813698", "exception": false, "start_time": "2024-04-27T05:36:01.760362", "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": "54f1b985", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ac3cf1fe-d39d-48bb-a31d-e3ee0d70418b", "papermill": { "duration": 0.046957, "end_time": "2024-04-27T05:36:01.907077", "exception": false, "start_time": "2024-04-27T05:36:01.860120", "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": "aac86418", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:02.002729Z", "iopub.status.busy": "2024-04-27T05:36:02.002103Z", "iopub.status.idle": "2024-04-27T05:36:02.006968Z", "shell.execute_reply": "2024-04-27T05:36:02.006295Z" }, "executionStartTime": 1628191319191, "executionStopTime": 1628191319220, "hidden_ranges": [], "originalKey": "9fdb11b6-7845-4f06-90fd-527fee088d76", "papermill": { "duration": 0.054013, "end_time": "2024-04-27T05:36:02.008346", "exception": false, "start_time": "2024-04-27T05:36:01.954333", "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": "196d66bb", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:02.102842Z", "iopub.status.busy": "2024-04-27T05:36:02.102377Z", "iopub.status.idle": "2024-04-27T05:36:02.105841Z", "shell.execute_reply": "2024-04-27T05:36:02.105225Z" }, "executionStartTime": 1628191321755, "executionStopTime": 1628191321791, "hidden_ranges": [], "originalKey": "27065b03-7234-49c1-b3ae-f6442ec4e3d6", "papermill": { "duration": 0.052349, "end_time": "2024-04-27T05:36:02.107089", "exception": false, "start_time": "2024-04-27T05:36:02.054740", "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": "cdb5409b", "metadata": { "execution": { "iopub.execute_input": "2024-04-27T05:36:02.202214Z", "iopub.status.busy": "2024-04-27T05:36:02.201592Z", "iopub.status.idle": "2024-04-27T05:36:02.205479Z", "shell.execute_reply": "2024-04-27T05:36:02.204846Z" }, "executionStartTime": 1628191323464, "executionStopTime": 1628191323491, "originalKey": "c58b70de-06b5-4e03-8958-c3c55d4c295a", "papermill": { "duration": 0.052993, "end_time": "2024-04-27T05:36:02.206724", "exception": false, "start_time": "2024-04-27T05:36:02.153731", "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": "edaab5f2", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:02.302322Z", "iopub.status.busy": "2024-04-27T05:36:02.301760Z", "iopub.status.idle": "2024-04-27T05:36:02.305348Z", "shell.execute_reply": "2024-04-27T05:36:02.304696Z" }, "executionStartTime": 1628191325491, "executionStopTime": 1628191325519, "hidden_ranges": [], "originalKey": "4b1ce9ba-e2e5-4a8a-9c15-5d01a2940a55", "papermill": { "duration": 0.05289, "end_time": "2024-04-27T05:36:02.306578", "exception": false, "start_time": "2024-04-27T05:36:02.253688", "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": "85bb7f43", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "3b7b797c-2478-48d6-84ea-c62a886db31f", "papermill": { "duration": 0.04701, "end_time": "2024-04-27T05:36:02.400410", "exception": false, "start_time": "2024-04-27T05:36:02.353400", "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": "986ade43", "metadata": { "execution": { "iopub.execute_input": "2024-04-27T05:36:02.496560Z", "iopub.status.busy": "2024-04-27T05:36:02.496044Z", "iopub.status.idle": "2024-04-27T05:36:02.499446Z", "shell.execute_reply": "2024-04-27T05:36:02.498752Z" }, "executionStartTime": 1628191328765, "executionStopTime": 1628191328792, "originalKey": "a52ace6c-8144-446b-97d5-2f27879ca187", "papermill": { "duration": 0.053229, "end_time": "2024-04-27T05:36:02.500751", "exception": false, "start_time": "2024-04-27T05:36:02.447522", "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": "97f1c2eb", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:02.595889Z", "iopub.status.busy": "2024-04-27T05:36:02.595391Z", "iopub.status.idle": "2024-04-27T05:36:02.598980Z", "shell.execute_reply": "2024-04-27T05:36:02.598320Z" }, "executionStartTime": 1628191330913, "executionStopTime": 1628191330991, "hidden_ranges": [], "originalKey": "9fd6ec68-4c53-4276-a98a-61431cdc05d5", "papermill": { "duration": 0.05286, "end_time": "2024-04-27T05:36:02.600334", "exception": false, "start_time": "2024-04-27T05:36:02.547474", "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": "f4bd39d7", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:02.695571Z", "iopub.status.busy": "2024-04-27T05:36:02.695104Z", "iopub.status.idle": "2024-04-27T05:36:02.698983Z", "shell.execute_reply": "2024-04-27T05:36:02.698401Z" }, "executionStartTime": 1628191334273, "executionStopTime": 1628191334299, "hidden_ranges": [], "originalKey": "a8eef6a6-1d53-494a-907f-10ca35492a8c", "papermill": { "duration": 0.053336, "end_time": "2024-04-27T05:36:02.700199", "exception": false, "start_time": "2024-04-27T05:36:02.646863", "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": "1ae14ba6", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "0c918735-9fda-4c36-90b5-163443e66c72", "papermill": { "duration": 0.046852, "end_time": "2024-04-27T05:36:02.793945", "exception": false, "start_time": "2024-04-27T05:36:02.747093", "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": "e09bd017", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:02.889079Z", "iopub.status.busy": "2024-04-27T05:36:02.888496Z", "iopub.status.idle": "2024-04-27T05:36:02.950264Z", "shell.execute_reply": "2024-04-27T05:36:02.949719Z" }, "executionStartTime": 1628191356513, "executionStopTime": 1628191356896, "hidden_ranges": [], "originalKey": "5ee13832-804a-413f-a6bc-1f8f96a817d8", "papermill": { "duration": 0.110889, "end_time": "2024-04-27T05:36:02.951626", "exception": false, "start_time": "2024-04-27T05:36:02.840737", "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": "a8932a20", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:03.046979Z", "iopub.status.busy": "2024-04-27T05:36:03.046449Z", "iopub.status.idle": "2024-04-27T05:36:09.871489Z", "shell.execute_reply": "2024-04-27T05:36:09.870779Z" }, "executionStartTime": 1628191362562, "executionStopTime": 1628191408255, "hidden_ranges": [], "originalKey": "0c6a6d44-29db-43dd-982d-dc664d00b009", "papermill": { "duration": 6.874516, "end_time": "2024-04-27T05:36:09.872955", "exception": false, "start_time": "2024-04-27T05:36:02.998439", "status": "completed" }, "requestMsgId": "8aca7b5b-aab8-4a39-9a49-d7b1e0c714c5", "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.aAgct3DTVU/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.aAgct3DTVU/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 04-27 05:36:03] 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.aAgct3DTVU/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.aAgct3DTVU/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 04-27 05:36:03] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.aAgct3DTVU/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: 6, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.aAgct3DTVU/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 04-27 05:36:04] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 7, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.aAgct3DTVU/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 04-27 05:36:04] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 8, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.aAgct3DTVU/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 04-27 05:36:04] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 9, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.aAgct3DTVU/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 04-27 05:36:05] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 10, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.aAgct3DTVU/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 04-27 05:36:05] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 11, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.aAgct3DTVU/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 04-27 05:36:05] ax.service.utils.report_utils: Column reason missing for all trials. 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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 04-27 05:36:09] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 23, HV: 34.79802134856089\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 04-27 05:36:09] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 34.79802134856089\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": "39c94e0f", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "767a7e9b-8902-424e-bfc4-f7afdba47302", "papermill": { "duration": 0.049609, "end_time": "2024-04-27T05:36:09.971942", "exception": false, "start_time": "2024-04-27T05:36:09.922333", "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": "a8fae710", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:10.072524Z", "iopub.status.busy": "2024-04-27T05:36:10.071932Z", "iopub.status.idle": "2024-04-27T05:36:10.133778Z", "shell.execute_reply": "2024-04-27T05:36:10.133059Z" }, "executionStartTime": 1628191422463, "executionStopTime": 1628191422803, "hidden_ranges": [], "originalKey": "8fc6bfb4-3012-4ce2-99ed-288378098c50", "papermill": { "duration": 0.114147, "end_time": "2024-04-27T05:36:10.135439", "exception": false, "start_time": "2024-04-27T05:36:10.021292", "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": "40bfa36c", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:10.235689Z", "iopub.status.busy": "2024-04-27T05:36:10.235026Z", "iopub.status.idle": "2024-04-27T05:36:59.774584Z", "shell.execute_reply": "2024-04-27T05:36:59.774040Z" }, "executionStartTime": 1628191425090, "executionStopTime": 1628191500240, "hidden_ranges": [], "originalKey": "27dd9425-b77e-4027-8412-30dd40c5abf1", "papermill": { "duration": 49.591267, "end_time": "2024-04-27T05:36:59.775933", "exception": false, "start_time": "2024-04-27T05:36:10.184666", "status": "completed" }, "requestMsgId": "65430b82-de1e-4946-9d8d-4a75762354c1", "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 04-27 05:36:11] 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 04-27 05:36:59] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 57.11672560654976\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": "9e329b00", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "e93178b6-5ba4-4c01-b8a2-e05971b7326f", "papermill": { "duration": 0.051326, "end_time": "2024-04-27T05:36:59.878829", "exception": false, "start_time": "2024-04-27T05:36:59.827503", "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": "a47b3524", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:36:59.983223Z", "iopub.status.busy": "2024-04-27T05:36:59.982893Z", "iopub.status.idle": "2024-04-27T05:37:19.496062Z", "shell.execute_reply": "2024-04-27T05:37:19.495342Z" }, "executionStartTime": 1628191505148, "executionStopTime": 1628191521900, "hidden_ranges": [], "originalKey": "71e013c5-638f-4ba4-bb9a-3e4a7d3eb9fa", "papermill": { "duration": 19.567105, "end_time": "2024-04-27T05:37:19.497459", "exception": false, "start_time": "2024-04-27T05:36:59.930354", "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": [ 0.11085465774230033, 0.11085465850868306, 0.05123663960509627, 0.04910520812721405, 0.11085465798179493, 0.05002533562393108, 0.04845756585876327, 0.0476857242949284, 0.08255568622660087, 0.06125136914720561, 0.04764204607679922, 0.05104959786509463, 0.04767038277045375, 0.07401208300399378, 0.05629875999343474, 0.07007455388624456, 0.04806510235481729, 0.05268385477423133, 0.06821980724701933, 0.11696893656602106 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "error_y": { "array": [ 0.00508946261069133, 0.005089462607242131, 0.0021630295532368694, 0.0021261858142100545, 0.00508946261069133, 0.002139075370995563, 0.0021794146027593426, 0.0021486951413115475, 0.003232010140300011, 0.002496260101168115, 0.0021359058880523487, 0.002294184173842867, 0.002132605056779089, 0.003077726238592271, 0.002574123705953295, 0.003092227003952732, 0.002168156917677144, 0.0023925168351508035, 0.002935194513571488, 0.004352453470723611 ], "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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"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": [ "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": "0a80d18d", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "77b2dbce-f1e4-443a-8f81-2e1cbe207301", "papermill": { "duration": 0.058777, "end_time": "2024-04-27T05:37:19.612270", "exception": false, "start_time": "2024-04-27T05:37:19.553493", "status": "completed" }, "tags": [] }, "source": [ "## qNParEGO\n", "This is a good alternative algorithm for multi-objective optimization when qNEHVI runs too slowly." ] }, { "cell_type": "code", "execution_count": 21, "id": "6ed517b8", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:37:19.725513Z", "iopub.status.busy": "2024-04-27T05:37:19.725210Z", "iopub.status.idle": "2024-04-27T05:37:19.786944Z", "shell.execute_reply": "2024-04-27T05:37:19.786352Z" }, "hidden_ranges": [], "originalKey": "2f796182-558b-47aa-8072-4dbf40123133", "papermill": { "duration": 0.119468, "end_time": "2024-04-27T05:37:19.788427", "exception": false, "start_time": "2024-04-27T05:37:19.668959", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "parego_experiment = build_experiment()\n", "parego_data = initialize_experiment(parego_experiment)" ] }, { "cell_type": "code", "execution_count": 22, "id": "8ad765b1", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:37:19.900764Z", "iopub.status.busy": "2024-04-27T05:37:19.900124Z", "iopub.status.idle": "2024-04-27T05:38:01.409753Z", "shell.execute_reply": "2024-04-27T05:38:01.409201Z" }, "hidden_ranges": [], "originalKey": "72999188-90f5-43e0-b1d9-d468e7d51191", "papermill": { "duration": 41.567392, "end_time": "2024-04-27T05:38:01.411177", "exception": false, "start_time": "2024-04-27T05:37:19.843785", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 04-27 05:37:20] 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 04-27 05:37:21] 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 04-27 05:37:22] 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 04-27 05:37:23] 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 04-27 05:37:25] 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 04-27 05:37:27] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 5, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 04-27 05:37:28] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 6, HV: 0.0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[WARNING 04-27 05:37:29] ax.service.utils.report_utils: Column reason missing for all trials. Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 7, HV: 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", "[WARNING 04-27 05:37:30] ax.service.utils.report_utils: Column reason missing for all trials. 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Not appending column.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 24, HV: 47.11642649612552\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", "id": "a8c4a042", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "67ded85f-7c58-4c31-8df5-b0d8d07e4299", "papermill": { "duration": 0.057557, "end_time": "2024-04-27T05:38:01.526380", "exception": false, "start_time": "2024-04-27T05:38:01.468823", "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": "6fa757a2", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:38:01.642871Z", "iopub.status.busy": "2024-04-27T05:38:01.642358Z", "iopub.status.idle": "2024-04-27T05:38:20.698743Z", "shell.execute_reply": "2024-04-27T05:38:20.698067Z" }, "hidden_ranges": [], "originalKey": "3b1f39fd-ef75-4ea4-865b-f7b54b90da07", "papermill": { "duration": 19.116451, "end_time": "2024-04-27T05:38:20.700440", "exception": false, "start_time": "2024-04-27T05:38:01.583989", "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": [ 0.02925777417932354, 0.021143729897229686, 0.018860941540750013, 0.021574700472454477, 0.03338110537939655, 0.029257774348679075, 0.02989284861806828, 0.016991570283715854, 0.01710716806036756, 0.04022279063622869, 0.03028301441788079, 0.019346292035617944, 0.025065374891987513, 0.0331181310299675, 0.027730601802507943, 1.3639737861533634, 0.027117757746267835, 0.02812709586120387, 0.041816097323744035, 1.419673351284611 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "error_y": { "array": [ 0.003431827183109502, 0.002203250376106273, 0.002085795845883887, 0.0025070656206036745, 0.002837842124656852, 0.0034318271719125104, 0.002625937987988234, 0.0018327788058725464, 0.00183396625306286, 0.003395290927835369, 0.002967298085866272, 0.001988150128135667, 0.0023938457354603124, 0.0027980721516654293, 0.002521394826403703, 0.06565450185627957, 0.0027298339807140955, 0.0028984542065272428, 0.005095813776334413, 0.06809418684765244 ], "color": "rgba(128,177,211,0.4)", "thickness": 2, "type": "data" }, "hoverinfo": "text", "legendgroup": "mean", "marker": { "color": "rgba(128,177,211,1)" }, "mode": "markers", "name": "mean", "text": [ "Parameterization 0
a: -17.507 [-17.537, -17.478]
b: -1.18 [-1.184, -1.177]

Parameterization:
x1: 0.0
x2: 0.9999999999999983", "Parameterization 1
a: -13.06 [-13.081, -13.039]
b: -1.78 [-1.783, -1.778]

Parameterization:
x1: 0.014737898755638194
x2: 1.0", "Parameterization 2
a: -13.41 [-13.429, -13.391]
b: -1.73 [-1.732, -1.728]

Parameterization:
x1: 0.013479116408296254
x2: 1.0", "Parameterization 3
a: -16.769 [-16.791, -16.748]
b: -1.274 [-1.276, -1.271]

Parameterization:
x1: 0.0022877667126486767
x2: 0.9999999999999998", "Parameterization 4
a: -10.73 [-10.763, -10.696]
b: -2.138 [-2.141, -2.135]

Parameterization:
x1: 0.0237283314439537
x2: 0.9999999999999999", "Parameterization 5
a: -17.507 [-17.537, -17.478]
b: -1.18 [-1.184, -1.177]

Parameterization:
x1: 1.567845859928955e-17
x2: 0.9999999999999993", "Parameterization 6
a: -11.877 [-11.907, -11.847]
b: -1.957 [-1.960, -1.955]

Parameterization:
x1: 0.019154753795491773
x2: 1.0", "Parameterization 7
a: -15.007 [-15.024, -14.990]
b: -1.506 [-1.508, -1.505]

Parameterization:
x1: 0.007976203079850669
x2: 1.0", "Parameterization 8
a: -15.052 [-15.070, -15.035]
b: -1.5 [-1.502, -1.498]

Parameterization:
x1: 0.007825859577901925
x2: 0.9999999999999999", "Parameterization 9
a: -6.968 [-7.008, -6.927]
b: -2.826 [-2.829, -2.823]

Parameterization:
x1: 0.04193643368619931
x2: 1.0", "Parameterization 10
a: -7.74 [-7.771, -7.710]
b: -2.668 [-2.671, -2.665]

Parameterization:
x1: 0.037617413032533256
x2: 1.0", "Parameterization 11
a: -15.931 [-15.950, -15.911]
b: -1.383 [-1.385, -1.381]

Parameterization:
x1: 0.004951443882276548
x2: 1.0", "Parameterization 12
a: -12.542 [-12.567, -12.517]
b: -1.857 [-1.859, -1.854]

Parameterization:
x1: 0.016639370031686418
x2: 0.9999999999999999", "Parameterization 13
a: -11.15 [-11.183, -11.117]
b: -2.071 [-2.074, -2.068]

Parameterization:
x1: 0.02201715668831928
x2: 1.0", "Parameterization 14
a: -12.192 [-12.219, -12.164]
b: -1.909 [-1.912, -1.907]

Parameterization:
x1: 0.017954079931223343
x2: 1.0", "Parameterization 15
a: -3.364 [-4.728, -2.000]
b: -3.98 [-4.046, -3.914]

Parameterization:
x1: 0.07743684449138495
x2: 1.0", "Parameterization 16
a: -9.459 [-9.486, -9.431]
b: -2.351 [-2.354, -2.349]

Parameterization:
x1: 0.029213909896893504
x2: 1.0", "Parameterization 17
a: -7.893 [-7.921, -7.865]
b: -2.638 [-2.641, -2.636]

Parameterization:
x1: 0.036809523612184473
x2: 0.9999999999999999", "Parameterization 18
a: -5.866 [-5.908, -5.824]
b: -3.076 [-3.081, -3.071]

Parameterization:
x1: 0.048988702128398384
x2: 1.0", "Parameterization 19
a: -3.342 [-4.761, -1.922]
b: -3.999 [-4.067, -3.931]

Parameterization:
x1: 0.07809356743573313
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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": "778f2336", "metadata": { "code_folding": [], "collapsed": true, "hidden_ranges": [], "originalKey": "a67f7345-1777-4372-8704-bb80c4c4e783", "papermill": { "duration": 0.0618, "end_time": "2024-04-27T05:38:20.824043", "exception": false, "start_time": "2024-04-27T05:38:20.762243", "status": "completed" }, "tags": [] }, "source": [ "## Plot empirical data" ] }, { "cell_type": "markdown", "id": "f6213066", "metadata": { "code_folding": [], "collapsed": true, "hidden_ranges": [], "originalKey": "de878adc-0eb2-4599-8c1b-e0adbc0c0765", "papermill": { "duration": 0.06098, "end_time": "2024-04-27T05:38:20.946055", "exception": false, "start_time": "2024-04-27T05:38:20.885075", "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": "51744364", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:38:21.069875Z", "iopub.status.busy": "2024-04-27T05:38:21.069172Z", "iopub.status.idle": "2024-04-27T05:38:23.414465Z", "shell.execute_reply": "2024-04-27T05:38:23.413772Z" }, "hidden_ranges": [], "originalKey": "c6296697-ef07-422d-b965-35e4e5104a12", "papermill": { "duration": 2.408614, "end_time": "2024-04-27T05:38:23.415840", "exception": false, "start_time": "2024-04-27T05:38:21.007226", "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": "e26145a7", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ca12287f-c7b8-4ef8-8eb9-57760eda5fed", "papermill": { "duration": 0.061522, "end_time": "2024-04-27T05:38:23.539349", "exception": false, "start_time": "2024-04-27T05:38:23.477827", "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": "d96e322b", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ec8b764b-c27d-4722-9e3d-d81cebb3624a", "papermill": { "duration": 0.061406, "end_time": "2024-04-27T05:38:23.662319", "exception": false, "start_time": "2024-04-27T05:38:23.600913", "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": "983fd65c", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-04-27T05:38:23.787952Z", "iopub.status.busy": "2024-04-27T05:38:23.787198Z", "iopub.status.idle": "2024-04-27T05:38:23.970189Z", "shell.execute_reply": "2024-04-27T05:38:23.969513Z" }, "hidden_ranges": [], "originalKey": "d50b98bc-5ab1-4826-a5b2-474a13f4bae0", "papermill": { "duration": 0.247326, "end_time": "2024-04-27T05:38:23.971571", "exception": false, "start_time": "2024-04-27T05:38:23.724245", "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\")" ] }, { "cell_type": "code", "execution_count": null, "id": "376cbafa", "metadata": { "papermill": { "duration": 0.062046, "end_time": "2024-04-27T05:38:24.095888", "exception": false, "start_time": "2024-04-27T05:38:24.033842", "status": "completed" }, "tags": [] }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.14" }, "papermill": { "default_parameters": {}, "duration": 208.11173, "end_time": "2024-04-27T05:38:25.532000", "environment_variables": {}, "exception": null, "input_path": "/tmp/tmp.aAgct3DTVU/Ax-main/tutorials/multiobjective_optimization.ipynb", "output_path": "/tmp/tmp.aAgct3DTVU/Ax-main/tutorials/multiobjective_optimization.ipynb", "parameters": {}, "start_time": "2024-04-27T05:34:57.420270", "version": "2.6.0" } }, "nbformat": 4, "nbformat_minor": 5 }