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This research advances parallel Gaussian process bandit optimization by eliminating the multiplicative regret penalty associated with batch size, removing the need for an often ineffective initial uncertainty sampling phase. The findings demonstrate superior performance in noiseless settings compared to noisy ones, offering a more efficient theoretical framework for sequential decision-making algorithms.
Improved Regret Analysis for Parallel Gaussian Process Bandit Optimization
arXiv:2608.16492v1 Announce Type: cross Abstract: This paper studies the regret analysis for parallel Gaussian process (GP) bandit optimization. The known regret upper bounds for the widely used GP batched upper confidence bound and GP batched Thompson sampling (GP-BTS) suffer from a multiplicative factor with respect to the batch size $Q$. To avoid this degradation, existing analyses require a polynomial number of uncertainty sampling (US) for $Q$ at the beginning of optimization. However, this initial US phase is often ineffective in practice. This paper shows that the regret upper bound without the multiplicative factor on $Q$ can be achieved without the initial US phase, using GP-BTS as an example. Furthermore, we show much better regret upper bounds in the noiseless setting than in the noisy setting, as in the sequential GP bandit setting.
Abstract:This paper studies the regret analysis for parallel Gaussian process (GP) bandit optimization. The known regret upper bounds for the widely used GP batched upper confidence bound and GP batched Thompson sampling (GP-BTS) suffer from a multiplicative factor with respect to the batch size $Q$. To avoid this degradation, existing analyses require a polynomial number of uncertainty sampling (US) for $Q$ at the beginning of optimization. However, this initial US phase is often ineffective in practice. This paper shows that the regret upper bound without the multiplicative factor on $Q$ can be achieved without the initial US phase, using GP-BTS as an example. Furthermore, we show much better regret upper bounds in the noiseless setting than in the noisy setting, as in the sequential GP bandit setting.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2608.16492 [stat.ML]
(or arXiv:2608.16492v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2608.16492 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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