改进并行高斯过程优化的后悔值分析，无需初始无效采样阶段。
Improved Regret Analysis for Parallel Gaussian Process Bandit Optimization
- 通过改进GP-BTS算法，避免了批处理大小带来的后悔值恶化。
- 在无噪声情况下，后悔值上界显著优于有噪声情况。
- 适用于追求高效并行优化的机器学习研究者。
本文研究并行高斯过程（GP）带宽优化的后悔值分析。现有的GP批量上置信界和GP批量汤普森采样（GP-BTS）的后悔值上界存在与批处理大小 $Q$ 的乘法因子，导致性能下降。为避免此问题，已有分析要求在优化初期进行多项式数量的不确定性采样（US），但该阶段在实践中常无效。本文证明，无需初始US阶段即可实现不依赖 $Q$ 的后悔值上界，以GP-BTS为例。此外，在无噪声环境下，其后悔值上界明显优于有噪声环境，与序列式GP带宽设置一致。
原文摘要 · Abstract (English)
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.
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