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This paper focuses on solving a data-driven distributionally robustoptimization problem over a network of agents. The agents aim to minimize theworst-case expected cost computed over a Wasserstein ambiguity set that iscentered at the empirical distribution. The samples of the uncertainty aredistributed across the agents. Our approach consists of reformulating theproblem as a semi-infinite program and then designing a distributed algorithmthat solves a generic semi-infinite problem that has the same informationstructure as the reformulated problem. In particular, the decision variablesconsist of both local ones that agents are free to optimize over and globalones where they need to agree on. Our distributed algorithm is an iterativeprocedure that combines the notions of distributed ADMM and the cutting-surfacemethod. We show that the iterates converge asymptotically to a solution of thedistributionally robust problem to any pre-specified accuracy. Simulationsillustrate our results.

Data-driven distributionally robust optimization over a network via distributed semi-infinite programming