Batch Bayesian optimisation via density-ratio estimation with guarantees

TL;DR

This paper introduces a theoretically grounded batch Bayesian optimisation method based on density-ratio estimation, enhancing scalability and uncertainty estimation, with proven performance guarantees and empirical validation against existing methods.

Contribution

It extends the BORE framework to batch optimisation with theoretical guarantees and improved uncertainty estimates, advancing scalable Bayesian optimisation techniques.

Findings

The proposed method achieves competitive performance in batch BO tasks.

Theoretical regret bounds are established for the new algorithms.

Empirical results demonstrate improved scalability and uncertainty estimation.

Abstract

Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points via an acquisition function and a prior over functions, such as a Gaussian process. Recently, however, a reformulation of BO via density-ratio estimation (BORE) allowed reinterpreting the acquisition function as a probabilistic binary classifier, removing the need for an explicit prior over functions and increasing scalability. In this paper, we present a theoretical analysis of BORE's regret and an extension of the algorithm with improved uncertainty estimates. We also show that BORE can be naturally extended to a batch optimisation setting by recasting the problem as approximate Bayesian inference. The resulting algorithms come equipped with theoretical performance guarantees and are assessed against other batch and sequential BO baselines in a series of experiments.