arXiv:2608.13133stat.MLcs.LG2026-08

分析鲁棒学习在分布偏移下的统计性质,给出实际环境中的泛化误差保障。

Statistical Properties of Robust Learning under Distributional Shifts

论文配图:Statistical Properties of Robust Learning under Distributional Shifts
图 1 · 摘自论文原文
  • 推导出DRO和RS在目标分布下的有限样本误差界,揭示鲁棒性与正则化权衡。
  • 在已知偏移程度时,提出定向超参数调节方法,使两者表现互补。
  • 应用于需求预测问题,解释鲁棒策略如何应对需求分布上升。

分布偏移指部署环境与训练数据来源环境不一致。现有鲁棒学习框架如分布鲁棒优化(DRO)和鲁棒满意(RS)虽旨在应对此挑战,但其在有限样本下于目标环境的泛化误差保证及系统性比较仍不充分:现有分析多局限于源环境或对模糊集内最坏情况提供保障。本文转而研究目标环境中的泛化误差——即在分布偏移下的超额损失。贡献有三:第一,为DRO和RS在目标分布中推导出有限样本泛化误差界,明确刻画了降低对偏移敏感度与方法鲁棒性超参数带来的正则化惩罚之间的权衡,并避免了与Wasserstein经验集中相关的维数灾难;第二,当部分偏移信息如偏移幅度或方向可用时,提出信息导向的超参数校准方法,并在相同信息条件下对比两种方法;在此类部分信息情形下,DRO与RS表现出互补的理论与实证行为;第三,将该框架应用于网络补货量规划问题,解释鲁棒策略如何响应需求分布的正向偏移。上述结果填补了对鲁棒学习在分布偏移下统计性质的理解空白,为比较DRO与RS提供了严谨基础。

原文摘要 · Abstract (English)

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.

鲁棒学习分布偏移泛化误差优化

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。