Towards Regret Guarantees for One-Step Lookahead Bayesian Optimization

Abstract:This paper studies theoretical guarantees of a one-step lookahead Bayesian optimization (BO) method. 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 analyzes a one-step lookahead BO method, which we refer to as optimal-point variance reduction (OVR), that requires only posterior sampling and Monte Carlo approximations. We obtain a uniform Monte Carlo estimation error bound over an input domain in an acquisition function computation. Furthermore, we show that the regularized OVR, with a slight modification to facilitate exploration, achieves a vanishing Bayesian expected simple regret upper bound. Finally, we validate the performance of OVR and regularized OVR through numerical experiments.

Machine Learning (cs.LG)

arXiv:2606.00956 [cs.LG]

(or arXiv:2606.00956v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.00956 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.