Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee
2026-05-31 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study a way to improve Bayesian optimization by looking one step ahead, focusing on a method called optimal-point variance reduction (OVR). Unlike other similar methods that need hard calculations, their approach uses easier techniques like sampling and approximations. They prove that their method can reliably estimate values and show that a version with added exploration steadily gets better over time. Finally, they test this method with experiments to show it works well.
Bayesian optimizationone-step lookaheadposterior samplingMonte Carlo approximationuniform error boundexpected simple regretvariance reductionexploration-exploitation
Authors
Shion Takeno
Abstract
This paper studies a one-step lookahead Bayesian optimization (BO) method and its theoretical guarantee. Although the empirical effectiveness of one-step lookahead BO methods, such as entropy search, has been studied extensively, they often rely on computationally intractable approximations, and their regret guarantees remain underdeveloped. Thus, this paper proposes a one-step lookahead BO method called optimal-point variance reduction (OVR), which requires only posterior sampling and Monte Carlo approximations. We obtain a uniform error bound over an input domain for the Monte Carlo estimation in OVR. Furthermore, we show that the regularized OVR, with the slight modification to promote exploration, achieves a vanishing Bayesian expected simple regret upper bound. Finally, we demonstrate the effectiveness of OVR through numerical experiments.