A Bi-Objective Optimization Based Acquisition Strategy for Batch Bayesian Global Optimization

Abstract

In this paper, we deal with batch Bayesian Optimization (Bayes-Opt) problems over a box and we propose a novel bi-objective optimization (BOO) acquisition strategy to sample points where to evaluate the objective function. The BOO problem involves the Gaussian Process posterior mean and variance functions, which, in most of the acquisition strategies from the literature, are generally used in combination, frequently through scalarization. However, such scalarization could compromise the Bayes-Opt process performance, as getting the desired trade-off between exploration and exploitation is not trivial in most cases. We instead aim to reconstruct the Pareto front of the BOO problem based on optimizing both the posterior mean as well as the variance, thus generating multiple trade-offs without any a priori knowledge. The reconstruction is performed through the Non-dominated Sorting Memetic Algorithm (NSMA), recently proposed in the literature and proved to be effective in solving hard MOO problems. Finally, we present two clustering approaches, each of them operating on a different space, to select potentially optimal points from the Pareto front. We compare our methodology with well-known acquisition strategies from the literature, showing its effectiveness on a wide set of experiments.

References in corpus (13)

• A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
• A Literature Survey of Benchmark Functions For Global Optimization Problems
• Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design
• Bayesian optimization for materials design
• An Efficient Batch Constrained Bayesian Optimization Approach for Analog Circuit Synthesis via Multi-objective Acquisition Ensemble
• Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation
• SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes
• Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration
• The reparameterization trick for acquisition functions
• Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlow
• A Memetic Procedure for Global Multi-Objective Optimization
• Vanilla Bayesian Optimization Performs Great in High Dimensions
• Quantifying uncertainty with ensembles of surrogates for blackbox optimization

Cited by in corpus (1)

• Scalable Batch Bayesian Optimization Via Subspace Acquisition Functions