Improved Regret Analysis for Parallel Gaussian Process Bandit Optimization
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.
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