提出新方法同时求解鲁棒决策与最差分布，提升模型抗风险能力。
Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimization
- 从原始视角重构建模，将问题转为双层优化
- 设计双循环与单循环采样算法，理论可保证收敛
- 能直接生成压力测试场景，适合安全关键应用
分布鲁棒优化（DRO）是应对不确定性的有力框架。本文研究基于Sinkhorn差异（一种熵正则化Wasserstein距离）定义的模糊集的DRO，即Sinkhorn DRO。现有工作多从对偶角度出发，将其视为条件随机优化问题，适用多种随机梯度方法，但理论分析常依赖损失函数有界性，且难以直接获得最差分布。本文从原始视角重新建模，将问题转化为包含多个无限维下层子问题的双层规划。该形式可同时求得最优鲁棒决策与最差分布，在生成压力测试场景或设计鲁棒学习算法中极具价值。本文提出具有理论保证的双循环与单循环采样算法求解该双层问题，并在对抗分类任务的数值实验中验证了方法有效性。
原文摘要 · Abstract (English)
Distributionally robust optimization (DRO) has emerged as a powerful paradigm for reliable decision-making under uncertainty. This paper focuses on DRO with ambiguity sets defined via the Sinkhorn discrepancy: an entropy-regularized Wasserstein distance, referred to as Sinkhorn DRO. Existing work primarily addresses Sinkhorn DRO from a dual perspective, leveraging its formulation as a conditional stochastic optimization problem, for which many stochastic gradient methods are applicable. However, the theoretical analyses of such methods often rely on the boundedness of the loss function, and it is indirect to obtain the worst-case distribution associated with Sinkhorn DRO. In contrast, we study Sinkhorn DRO from the primal perspective, by reformulating it as a bilevel program with several infinite-dimensional lower-level subproblems over probability space. This formulation enables us to simultaneously obtain the optimal robust decision and the worst-case distribution, which is valuable in practical settings, such as generating stress-test scenarios or designing robust learning algorithms. We propose both double-loop and single-loop sampling-based algorithms with theoretical guarantees to solve this bilevel program. Finally, we demonstrate the effectiveness of our approach through a numerical study on adversarial classification.
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