在不确定环境下优化黑箱函数，用新算法实现高效稳健决策
Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context
- 基于Wasserstein距离构建不确定性集，支持连续上下文分布
- 理论证明可达到近似最优的亚线性后悔界
- 适用于实际场景中的复杂优化问题，计算高效易实现
我们解决在上下文分布不确定性下的序列数据驱动决策挑战。该问题广泛存在于现实场景中，学习者需在不可控上下文变量影响下优化黑箱目标函数。本文考虑上下文分布虽不确定，但已知位于基于Wasserstein距离定义的模糊集内的情形。提出一种新型的Wasserstein分布鲁棒贝叶斯优化算法，可在保持计算可处理性的前提下处理连续上下文分布。理论分析结合希尔伯特空间中的自归一化浓度结果与分布鲁棒优化的有限样本边界，建立了匹配当前最优水平的亚线性后悔界。通过在合成与真实世界问题上的大量对比实验，验证了所提方法的简洁性、有效性与实用性。
原文摘要 · Abstract (English)
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of uncontrollable contextual variables. We consider the setting where the context distribution is uncertain but known to lie within an ambiguity set defined as a ball in the Wasserstein distance. We propose a novel algorithm for Wasserstein Distributionally Robust Bayesian Optimization that can handle continuous context distributions while maintaining computational tractability. Our theoretical analysis combines recent results in self-normalized concentration in Hilbert spaces and finite-sample bounds for distributionally robust optimization to establish sublinear regret bounds that match state-of-the-art results. Through extensive comparisons with existing approaches on both synthetic and real-world problems, we demonstrate the simplicity, effectiveness, and practical applicability of our proposed method.
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