Improved Regret Analysis for Parallel Gaussian Process Bandit Optimization

2026-08-17

AI Summary

This study addresses the degradation of regret bounds with batch size and their dependence on initial sampling in parallel Gaussian process bandit optimization. We propose an improved GP-BTS algorithm that eliminates the multiplicative effect of the batch factor on regret bounds without requiring an initial uncertainty sampling phase. Theoretical analysis demonstrates that this method achieves significantly tighter regret upper bounds in noiseless settings compared to noisy scenarios. By establishing batch-size-independent regret guarantees and revealing distinct theoretical advantages in noiseless environments, this work provides a superior theoretical foundation and algorithmic paradigm for parallel Bayesian optimization.

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.

Problem

• Parallel Gaussian Process Bandit Optimization
• Regret Analysis
• Batch Size Degradation
• Uncertainty Sampling

Innovation

• Parallel Gaussian Process Bandit
• Regret Analysis
• Batched Thompson Sampling
• Uncertainty Sampling
• Noiseless Setting