Robust Stochastic Optimization Made Easy with RSOME

TLDR

The authors introduce a distributionally robust optimization model, RSO, and an accompanying modeling package, RSOME, to unify scenario-tree-based stochastic linear optimization and distributionally robust optimization. RSO employs event-wise recourse adaptations that combine scenario-tree and affine strategies, and an event-wise ambiguity set that encompasses traditional and machine-learning-based ambiguity formulations. The paper presents several RSO models, such as Hurwicz-criterion optimization and two-stage Wasserstein-ambiguity problems. The paper was accepted by David Simchi‑Levi, Optimization.

Abstract

We present a new distributionally robust optimization model called robust stochastic optimization (RSO), which unifies both scenario-tree-based stochastic linear optimization and distributionally robust optimization in a practicable framework that can be solved using the state-of-the-art commercial optimization solvers. We also develop a new algebraic modeling package, Robust Stochastic Optimization Made Easy (RSOME), to facilitate the implementation of RSO models. The model of uncertainty incorporates both discrete and continuous random variables, typically assumed in scenario-tree-based stochastic linear optimization and distributionally robust optimization, respectively. To address the nonanticipativity of recourse decisions, we introduce the event-wise recourse adaptations, which integrate the scenario-tree adaptation originating from stochastic linear optimization and the affine adaptation popularized in distributionally robust optimization. Our proposed event-wise ambiguity set is rich enough to capture traditional statistic-based ambiguity sets with convex generalized moments, mixture distribution, φ-divergence, Wasserstein (Kantorovich-Rubinstein) metric, and also inspire machine-learning-based ones using techniques such as K-means clustering and classification and regression trees. Several interesting RSO models, including optimizing over the Hurwicz criterion and two-stage problems over Wasserstein ambiguity sets, are provided. This paper was accepted by David Simchi-Levi, optimization.