TS-RSR: A provably efficient approach for batch Bayesian Optimization

TL;DR

This paper introduces TS-RSR, a novel batch Bayesian Optimization method that efficiently balances exploration and exploitation, with proven convergence guarantees and superior empirical performance on various test functions.

Contribution

The paper proposes a new sampling strategy for batch BO that minimizes regret-to-uncertainty ratio, providing theoretical guarantees and improved empirical results.

Findings

Achieves state-of-the-art performance on synthetic and real test functions.

Provides rigorous convergence guarantees for the proposed algorithm.

Outperforms several benchmark batch BO algorithms in experiments.

Abstract

This paper presents a new approach for batch Bayesian Optimization (BO) called Thompson Sampling-Regret to Sigma Ratio directed sampling (TS-RSR), where we sample a new batch of actions by minimizing a Thompson Sampling approximation of a regret to uncertainty ratio. Our sampling objective is able to coordinate the actions chosen in each batch in a way that minimizes redundancy between points whilst focusing on points with high predictive means or high uncertainty. Theoretically, we provide rigorous convergence guarantees on our algorithm's regret, and numerically, we demonstrate that our method attains state-of-the-art performance on a range of challenging synthetic and realistic test functions, where it outperforms several competitive benchmark batch BO algorithms.