Active Bayesian Optimization: Minimizing Minimizer Entropy

TL;DR

This paper introduces a new active Bayesian optimization method that focuses on reducing uncertainty about the function's minimizer, effectively handling multiple minimizers and improving accuracy over traditional criteria.

Contribution

It proposes a novel criterion based on minimizer entropy reduction and an efficient approximation, advancing Bayesian optimization techniques.

Findings

Accurately identifies the global minimizer.

Effectively incorporates multiple minimizers.

Outperforms conventional Bayesian optimization criteria.

Abstract

The ultimate goal of optimization is to find the minimizer of a target function.However, typical criteria for active optimization often ignore the uncertainty about the minimizer. We propose a novel criterion for global optimization and an associated sequential active learning strategy using Gaussian processes.Our criterion is the reduction of uncertainty in the posterior distribution of the function minimizer. It can also flexibly incorporate multiple global minimizers. We implement a tractable approximation of the criterion and demonstrate that it obtains the global minimizer accurately compared to conventional Bayesian optimization criteria.