{"ID":2922235,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-03T00:47:32.987482086Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.00956","arxiv_id":"2606.00956","title":"Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee","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.","short_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...","url_abs":"https://arxiv.org/abs/2606.00956","url_pdf":"https://arxiv.org/pdf/2606.00956v1","authors":"[\"Shion Takeno\"]","published":"2026-05-31T02:16:21Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"LoRA\"]","has_code":false}