Optimal Transport-Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes

• 成果类型: Article
• 署名作者: Blanchet, Jose; Murthy, Karthyek; Zhang, Fan
• 署名单位: Stanford University; Singapore University of Technology & Design
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1178
• 发表日期: 2022
• 页码: 1500-1529
• 关键词: stochastic-approximation; PROGRAMS

摘要

We consider optimal transport-based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss function, we obtain structural results about the value function, the optimal policy, and the worst-case optimal transport adversarial model. These results expose a rich structure embedded in the DRO problem (e.g., strong convexity even if the non-DRO problem is not strongly convex, a suitable scaling of the Lagrangian for the DRO constraint, etc., which are crucial for the design of efficient algorithms). As a consequence of these results, one can develop efficient optimization procedures that have the same sample and iteration complexity as a natural non-DRO benchmark algorithm, such as stochastic gradient descent.