Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimization

TMLR Paper5357 Authors

Abstract: Bayesian optimization is a powerful tool for optimizing an expensive-to-evaluate black-box function. In particular, the effectiveness of expected improvement (EI) has been demonstrated in a wide range of applications. However, theoretical analyses of EI are limited compared with other theoretically established algorithms. This paper analyzes a randomized variant of EI, which evaluates the EI from the maximum of the posterior sample path. We show that this posterior sampling-based random EI achieves the sublinear Bayesian cumulative regret bounds under the assumption that the black-box function follows a Gaussian process. Finally, we demonstrate the effectiveness of the proposed method through numerical experiments.

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Roman_Garnett1

Submission Number: 5357