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Robust Stochastic Optimization Made Easy with RSOME

Zhi Chen (chenzhi.james***at***gmail.com)
Melvyn Sim (melvynsim***at***gmail.com)
Peng Xiong (xiongpengnus***at***gmail.com)

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, 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 non-anticipativity 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, phi-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.

Keywords: stochastic linear optimization, distributionally robust optimization, machine learning

Category 1: Robust Optimization

Category 2: Stochastic Programming

Citation: Chen, Sim, Xiong (2020), forthcoming in Management Science.

Download: [PDF]

Entry Submitted: 06/02/2017
Entry Accepted: 06/02/2017
Entry Last Modified: 01/13/2020

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