AI 中文总结
针对Wasserstein分布鲁棒优化标准重表述含非凸子问题难求解的问题，提出收缩路径启发式算法，简化为一维搜索，实验表明其性能提升达Wasserstein DRO的85%-110%且计算成本低。
AI 中文摘要
Wasserstein分布鲁棒优化（DRO）是一种用于不确定性决策的通用且广泛采用的框架，但其标准确定性重表述通常包含难以求解的非凸内部子问题。为解决该问题，本文提出一种收缩路径启发式算法，将DRO问题的求解简化为在样本平均近似（SAA，通常性质良好）与经典鲁棒优化解（要求更高但实际可解）之间的线段上进行一维搜索。本文在简化场景中推导了先验次优性界，针对一般情况，通过对对偶形式应用类似启发式算法得到后验界。对多产品报童问题和预约调度问题的数值实验表明，收缩路径启发式算法达到了Wasserstein DRO相对于SAA的样本外性能提升的85%-110%（对应45%-70%），且计算成本仅为其一小部分。
英文摘要
Wasserstein distributionally robust optimization (DRO) is a versatile and widely adopted framework for decision-making under uncertainty, yet its standard deterministic reformulations generally contain non-convex inner subproblems that are challenging to solve. To address this issue, we propose a shrinkage path heuristic that reduces the solution of a DRO problem to a one-dimensional search over the line segment connecting the (typically benign) sample average approximation (SAA) and the (more demanding but practically solvable) classical robust optimization solution. We derive a priori suboptimality bounds in stylized settings and, for the general case, a posteriori bounds obtained by applying a similar heuristic to a dual formulation. Numerical experiments on a multi-item newsvendor and an appointment scheduling problem show that the shrinkage path heuristic attains 85-110% (resp. 45-70%) of the out-of-sample performance improvements of Wasserstein DRO over SAA, at a fraction of the computational cost.
