分布偏移下鲁棒学习的统计特性

中文摘要 AI 辅助

当目标部署环境与生成训练数据的源环境不同时，就会出现分布偏移。分布鲁棒优化（Distributionally Robust Optimization，DRO）和鲁棒满意（Robust Satisficing，RS）等鲁棒学习框架旨在应对这一挑战，但它们在这类偏移下的有限样本保证以及系统比较仍未得到充分探索：现有分析通常要么在源环境中建立保证，要么针对歧义集上的对抗最坏情况性能建立保证。本文转而研究目标环境中的泛化误差——即偏移后的目标分布下的超额损失。我们的贡献分为三部分。首先，我们推导了DRO和RS在偏移后的目标环境中的有限样本泛化误差界。这些界明确刻画了对偏移的敏感性降低与每种方法的鲁棒性超参数所诱导的正则化惩罚之间的权衡，并且避免了与Wasserstein经验集中相关的维数灾难。其次，当存在部分偏移信息（如偏移幅度或方向）时，我们提出了信息导向的超参数校准，并在给定相同信息的情况下比较这两种方法。在这些校准以及我们研究的部分信息 regime 下，DRO和RS表现出互补的理论和实证行为。最后，我们将该框架应用于网络批量规模问题，用它来解释鲁棒策略如何应对需求分布的正向偏移。总体而言，这些结果填补了对分布偏移下鲁棒学习方法统计特性理解的空白，并为比较DRO和RS提供了原则性基础。

英文摘要

Distributional shifts arise when the target deployment environment differs from the source environment that generated the training data. Robust learning frameworks such as Distributionally Robust Optimization (DRO) and Robust Satisficing (RS) aim to address this challenge, yet their finite-sample guarantees under such shifts, and their systematic comparison, remain underexplored: existing analyses typically establish guarantees either in the source environment or for adversarial worst-case performance over an ambiguity set. This paper instead studies generalization error in the target environment---the excess loss under the shifted target distribution. Our contributions are threefold. First, we derive finite-sample generalization error bounds in the shifted target environment for both DRO and RS. These bounds explicitly characterize the trade-off between reduced sensitivity to shift and the regularization penalty induced by each method's robustness hyperparameter, and they avoid the curse of dimensionality associated with Wasserstein empirical concentration. Second, when partial shift information such as shift magnitude or direction is available, we propose information-directed hyperparameter calibrations and compare the two methods given the same information. Under these calibrations, and in the partial-information regimes we study, DRO and RS exhibit complementary theoretical and empirical behavior. Finally, we apply the framework to a network lot-sizing problem, using it to interpret how robust policies respond to positive shifts in the demand distribution. Together, these results fill a gap in understanding the statistical properties of robust learning methods under distributional shifts and provide a principled basis for comparing DRO and RS.

发表机构

• National University of Singapore（新加坡国立大学）
• Tsinghua University（清华大学）
• University College London（伦敦大学学院）

机构由 AI 辅助整理，请以论文原文为准。