A Shrinkage Path Heuristic for Wasserstein Distributionally Robust Optimization

Abstract

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.

Disclosure

“whereas the regularized SAA benchmarks (ℓ1 -RSAA-CV and ℓ2 -RSAA-CV) barely improve on SAA. Boxes, whiskers, and shaded bands follow the conventions of Figure 3. Use of Large Language Models Large language models (including Claude Fable 5 and Chat-GPT-Pro 5.6) were used to assist in writing the manuscript and implementing the numerical experiments. The authors have carefully reviewed and edited all generated content and take full responsibility fo”

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2026-08-23T05:15:16.158689Z

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