用根查找法提升高维贝叶斯优化中高斯过程采样的全局搜索效率
Gaussian Process Thompson Sampling via Rootfinding
- 通过单变量全局根查找定位先验样本的局部极值点，作为优化起点
- 在高维场景下显著提升后验样本全局优化成功率，加速收敛
- 适合需要高效全局搜索的高维贝叶斯优化任务，如超参调优
Thompson采样（TS）是一种简单高效的贝叶斯决策策略，通过从奖励分布的后验中采样并优化采样结果来选择动作。在连续优化中，目标函数的后验通常为高斯过程（GP），其样本路径存在大量局部极值，导致全局优化困难。本文提出一种针对GP-TS的高效全局优化策略：利用一维全局根查找识别先验样本的所有局部极值点，并基于可微分、解耦的表示形式优化后验样本。该方法在高维场景下显著提升了后验样本的全局优化性能，从而大幅改善了使用GP-TS获取函数的贝叶斯优化整体表现，出人意料地优于传统的GP-UCB和EI方法。
原文摘要 · Abstract (English)
Thompson sampling (TS) is a simple, effective stochastic policy in Bayesian decision making. It samples the posterior belief about the reward profile and optimizes the sample to obtain a candidate decision. In continuous optimization, the posterior of the objective function is often a Gaussian process (GP), whose sample paths have numerous local optima, making their global optimization challenging. In this work, we introduce an efficient global optimization strategy for GP-TS that carefully selects starting points for gradient-based multi-start optimizers. It identifies all local optima of the prior sample via univariate global rootfinding, and optimizes the posterior sample using a differentiable, decoupled representation. We demonstrate remarkable improvement in the global optimization of GP posterior samples, especially in high dimensions. This leads to dramatic improvements in the overall performance of Bayesian optimization using GP-TS acquisition functions, surprisingly outperforming alternatives like GP-UCB and EI.
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