Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee

Shion Takeno

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arXiv · 2606.00956

Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee

Shion Takeno

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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.

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BibTeX RIS

Shion Takeno. 2026-05-31. Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee. https://arxiv.org/abs/2606.00956

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