![]() ![]() filterwarnings ( "ignore", category = BadInitialCandidatesWarning ) warnings. Import time import warnings from botorch import fit_gpytorch_mll from botorch.exceptions import BadInitialCandidatesWarning from import SobolQMCNormalSampler from _objective.box_decompositions.dominated import ( DominatedPartitioning, ) from _objective.pareto import is_non_dominated warnings. randn_like ( new_obj_true ) * NOISE_SE return new_x, new_obj, new_obj_true bounds ) new_obj_true = problem ( new_x ) new_obj = new_obj_true + torch. The helper function below initializes the $q$EHVI acquisition function, optimizes it, and returns the batch $\, ) # observe new values new_x = unnormalize ( candidates. ![]() likelihood, model ) return mll, modelĭefine a helper functions that performs the essential BO step for $q$EHVI and $q$NEHVI ¶ append ( FixedNoiseGP ( train_x, train_y, train_yvar, outcome_transform = Standardize ( m = 1 ) ) ) model = ModelListGP ( * models ) mll = SumMarginalLogLikelihood ( model. ![]() full_like ( train_y, NOISE_SE ** 2 ) models. shape ): train_y = train_obj train_yvar = torch. bounds ) models = for i in range ( train_obj. randn_like ( train_obj_true ) * NOISE_SE return train_x, train_obj, train_obj_true def initialize_model ( train_x, train_obj ): # define models for objective and constraint train_x = normalize ( train_x, problem. squeeze ( 1 ) train_obj_true = problem ( train_x ) train_obj = train_obj_true + torch. ![]() tensor (, ** tkwargs ) def generate_initial_data ( n = 6 ): # generate training data train_x = draw_sobol_samples ( bounds = problem. Advances in Neural Information Processing Systems 34, 2021.įor batch optimization (or in noisy settings), we strongly recommend using $q$NEHVI rather than $q$EHVI because it is far more efficient than $q$EHVI and mathematically equivalent in the noiseless setting.įrom _regression import FixedNoiseGP from _list_gp_regression import ModelListGP from import Standardize from _marginal_log_likelihood import SumMarginalLogLikelihood from import unnormalize, normalize from import draw_sobol_samples NOISE_SE = torch. Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement. Advances in Neural Information Processing Systems 33, 2020. Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization. Since botorch assumes a maximization of all objectives, we seek to find the Pareto frontier, the set of optimal trade-offs where improving one metric means deteriorating another. The noise standard deviations are 15.19 and 0.63 for each objective, respectively. See botorch/test_functions/multi_objective.py for details on BraninCurrin. We use the parallel ParEGO ($q$ParEGO), parallel Expected Hypervolume Improvement ($q$EHVI), and parallel Noisy Expected Hypervolume Improvement ($q$NEHVI) acquisition functions to optimize a synthetic BraninCurrin problem test function with additive Gaussian observation noise over a 2-parameter search space ^2. If desired, this can also be customized by adding "botorch_acqf_class":, to the model_kwargs. Given a MultiObjective, Ax will default to the $q$NEHVI acquisiton function. If desired, you can use a custom BoTorch model in Ax, following the Using BoTorch with Ax tutorial. In general, we recommend using Ax for a simple BO setup like this one, since this will simplify your setup (including the amount of code you need to write) considerably. In this tutorial, we illustrate how to implement a simple multi-objective (MO) Bayesian Optimization (BO) closed loop in BoTorch. Noisy, Parallel, Multi-Objective BO in BoTorch with qEHVI, qNEHVI, and qNParEGO ¶ ![]()
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