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This paper addresses a gap in Bayesian optimization theory: cumulative regret bounds don't guarantee the quality of the final recommendation, which matters when evaluations are noisy. The proposed method occasionally swaps in exploration queries and uses fill distance to bound GP posterior uncertainty and, in turn, inference regret. Practitioners tuning hyperparameters or control policies should note that the empirical gains are shown on benchmarks and a control task, so transfer to other settings still needs testing.
Exploration strategies for Gaussian process bandit optimization with inference regret guarantees
arXiv:2610.16187v1 Announce Type: cross Abstract: Existing cumulative regret guarantees for Bayesian optimization (BO) do not necessarily characterize the quality of the algorithm's final output. This gap is critical under noisy evaluations, where the goal is to return a single high-quality recommendation. To address it, we introduce efficient exploration strategies that can be incorporated into any BO procedure by occasionally replacing the acquisition query with an exploration query. To validate this approach, we bound the Gaussian process posterior standard deviation over the search space via the fill distance of the queries, which measures the largest region left unexplored. We then use this result to derive upper bounds on the inference regret, i.e., the gap between the global optimum and the function value at the algorithm's returned point. Empirically, these exploration strategies improve the final recommendations of existing BO algorithms on synthetic benchmarks, hyperparameter optimization, and a control task.
Abstract:Existing cumulative regret guarantees for Bayesian optimization (BO) do not necessarily characterize the quality of the algorithm's final output. This gap is critical under noisy evaluations, where the goal is to return a single high-quality recommendation. To address it, we introduce efficient exploration strategies that can be incorporated into any BO procedure by occasionally replacing the acquisition query with an exploration query. To validate this approach, we bound the Gaussian process posterior standard deviation over the search space via the fill distance of the queries, which measures the largest region left unexplored. We then use this result to derive upper bounds on the inference regret, i.e., the gap between the global optimum and the function value at the algorithm's returned point. Empirically, these exploration strategies improve the final recommendations of existing BO algorithms on synthetic benchmarks, hyperparameter optimization, and a control task.
Machine Learning (stat.ML); Machine Learning (cs.LG); Optimization and Control (math.OC); Computation (stat.CO)
arXiv:2610.16187 [stat.ML]
(or arXiv:2610.16187v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.16187 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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