通过自适应缩小搜索空间，提升高维贝叶斯优化采样效率
Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization
- 基于代理模型梯度动态生成子空间候选点
- 在合成与真实任务中均显著优于传统方法
- 无需修改现有框架，可直接替换现有采样策略
在贝叶斯优化中，汤普森采样通过从目标函数最大值的后验分布中采样来选择评估点。由于高斯过程（GP）代理模型的后验采样问题难以解析求解，通常需依赖固定离散化候选点，但其密度随维度增加呈指数下降。以往工作通过可扩展的GP近似提高候选点密度，而本文提出正交思路：在采样过程中自适应缩小搜索空间。具体地，引入自适应候选点汤普森采样（ACTS），根据代理模型样本的梯度在子空间中生成候选点。ACTS是现有汤普森采样方法的简单即插即用替代方案——包括使用信任区域或其他局部近似的算法——能生成更优的最大值样本，并在合成与真实世界基准上实现更好优化性能。
原文摘要 · Abstract (English)
In Bayesian optimization, Thompson sampling selects the evaluation point by sampling from the posterior distribution over the objective function maximizer. Because this sampling problem is intractable for Gaussian process (GP) surrogates, the posterior distribution is typically restricted to fixed discretizations (i.e., candidate points) that become exponentially sparse as dimensionality increases. While previous works aim to increase candidate point density through scalable GP approximations, our orthogonal approach increases density by adaptively reducing the search space during sampling. Specifically, we introduce Adaptive Candidate Thompson Sampling (ACTS), which generates candidate points in subspaces guided by the gradient of a surrogate model sample. ACTS is a simple drop-in replacement for existing TS methods -- including those that use trust regions or other local approximations -- producing better samples of maxima and improved optimization across synthetic and real-world benchmarks.
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