让贝叶斯优化更智能：兼顾性能与平稳性，提升搜索效率
Beyond Objective-Based Improvement: Stationarity-Aware Expected Improvement for Bayesian Optimization
- 引入梯度范数改进目标函数，同时关注性能和局部最优接近度
- 在标准测试集上优于传统方法，尤其在收敛后期表现更优
- 适合需要精准定位最优解的复杂优化任务，如控制策略学习
贝叶斯优化（BO）是优化昂贵黑箱函数的有力框架，其中期望改进（EI）是最常用的采集函数。尽管其具有良好的实证表现，但EI忽略了的一阶最优性条件，仅依赖目标值的提升，导致在改进信号趋于平缓时失去指导能力，限制了搜索效率。本文提出基于梯度范数的期望改进（EI-GN），将一阶平稳性纳入改进准则，引导采样在高性能且接近平稳点的区域。我们推导出EI-GN的可计算闭式表达，并证明其仍保持改进型采集函数的合理性。通过嵌入向平稳点演进的进度，EI-GN提供了更丰富、更信息丰富的改进定义。在标准贝叶斯优化基准测试中，结果表明其持续优于基线方法，并进一步展示了其在控制策略学习中的适用性。
原文摘要 · Abstract (English)
Bayesian Optimization (BO) is a principled framework for optimizing expensive black-box functions, with Expected Improvement (EI) among its most widely used acquisition functions. Despite its empirical success, EI is agnostic to first-order optimality conditions, relying solely on objective-value improvement. As a result, it can exhibit vanishing acquisition signals where the improvement criterion is uninformative, limiting its effectiveness in guiding search. We propose Expected Improvement via Gradient Norms (EI-GN), a novel acquisition function that extends the improvement principle to incorporate first-order stationarity, promoting sampling in regions that are both high-performing and close to stationary points. We derive a tractable closed-form expression for EI-GN and show that it remains consistent with the improvement-based acquisition framework. By embedding progress toward stationarity into the acquisition criterion, EI-GN provides a richer and more informative notion of improvement. Empirical results on standard BO benchmarks demonstrate consistent gains over baseline methods, and we further illustrate its applicability to control policy learning.
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