Title: Non-Replacement Function Space Sampling for Bayesian Optimization
Primary area: optimization
Keywords: Non-replacement Function Space Sampling (NRFS), Bayesian Optimization, Probability of Optimality

Abstract: Bayesian optimization (BO) is a probabilistic framework for global optimization of expensive black-box functions, typically guided by an acquisition function that balances exploration and exploitation. We propose a novel acquisition strategy---Non-Replacement Function Space Sampling (NRFS). Instead of explicitly balancing the exploration–exploitation trade-off as in traditional BO methods, NRFS implicitly achieves this balance by prioritizing sampling functions from the function space that have not been involved in previous acquisition decisions. By establishing a correspondence between each candidate and the set of functions that consider it as the corresponding optimizer, we derive a principled and efficient searching strategy in the design space. We provide strong empirical evidence demonstrating that NRFS achieves state-of-the-art performance across a range of benchmark tasks, consistently improving optimization performance in all settings, particularly in challenging settings that demand both broad exploration and precise exploitation.