AI 中文总结
本文针对最优传输歧义集下DRO求解的扩展性问题，提出将内部最坏期望归约为标量预算分配的高效算法，结合神谕框架实现近似原始-对偶解，实验性能优于现有重构型求解器。
AI 中文摘要
最优传输歧义集下的分布鲁棒优化（DRO）传统上通过将极小极大问题重构为单级凸规划求解，虽理论上可处理，但这类重构会引入大量辅助变量和复杂的锥约束，实际应用中扩展性较差。本文通过将内部最坏情况期望问题精确归约为标量预算分配任务来解决这一挑战，该结构性洞见产生了一种高效算法，可绕过大规模提升型重构，同时配有快速后处理方案以恢复支撑点不超过N+1个的最优最坏情况分布，其中N为样本量。我们将该过程嵌入基于神谕的分布最优响应框架，直接计算整体DRO问题的近似原始-对偶解。此外，我们将分析扩展至对偶DRO形式，证明存在支撑原子数不超过min{N+n+1, KN}的最不利分布，其中n为决策维度，K为损失分量数，并提供高效凸规划归约以从原始DRO的解中提取该分布。数值实验表明，所提方法显著优于当前最先进的基于重构的求解器。
英文摘要
Distributionally robust optimization (DRO) with optimal transport ambiguity sets is traditionally solved by reformulating the minimax problem into a single-level convex program. While theoretically tractable, these reformulations introduce numerous auxiliary variables and demanding conic constraints that scale poorly in practice. In this paper, we address this challenge by reducing the inner worst-case expectation problem exactly to a scalar budget allocation task. This structural insight yields an efficient algorithm that bypasses large lifted reformulations, alongside a fast post-processing scheme to recover an optimal worst-case distribution supported on at most $N+1$ points, where $N$ denotes the sample size. We embed this procedure within an oracle-based distributional best-response framework to directly compute an approximate primal-dual solution to the overall DRO problem. Furthermore, we extend our analysis to the dual DRO formulation, proving the existence of a least-favorable distribution supported on at most $\min\{N+n+1, KN\}$ atoms, where $n$ and $K$ denote the decision dimension and number of loss components, respectively, and provide an efficient convex programming reduction to extract it from the solution of the primal DRO. Numerical experiments demonstrate that the proposed approach significantly outperforms state-of-the-art reformulation-based solvers.
