Regret

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Linear Regret

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O(T^Β)$ Simultaneous Regret

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Near-Optimal Regret Guarantees

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Mar 2, 2026 · cs.LGJ/K move · Enter open · S save

Randomized Kriging Believer for Parallel Bayesian Optimization with Regret Bounds

Shuhei Sugiura, Ichiro Takeuchi, Shion Takeno

Department of Engineering, Nagoya University, Aichi, Japan · RIKEN AIP, Tokyo, Japan

We consider the optimization problem of an expensive-to-evaluate black-box function, in which we can obtain noisy function values in parallel. For this problem, parallel Bayesian optimization (PBO) is a promising approach, which aims to optimize with fewer function evaluations by selecting a diverse input set for parallel evaluation. However, existing PBO methods suffer from poor practical performance or lack theoretical guarantees. In this study, we propose a PBO method, called randomized kriging believer (KB), based on a well-known KB heuristic and inheriting the advantages of the original KB: low computational complexity, a simple implementation, versatility across various BO methods, and applicability to asynchronous parallelization. Furthermore, we show that our randomized KB achieves Bayesian expected regret guarantees. We demonstrate the effectiveness of the proposed method through experiments, including those on real-data emulators.

Bayesian Optimization Gaussian Process Bayesian Parallel Heuristics Regret Black Box

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