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Data-driven Distributionally Robust Polynomial Optimization
Martin Mevissen · Emanuele Ragnoli · Jia Yuan Yu

Thu Dec 05 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor #None

We consider robust optimization for polynomial optimization problems where the uncertainty set is a set of candidate probability density functions. This set is a ball around a density function estimated from data samples, i.e., it is data-driven and random. Polynomial optimization problems are inherently hard due to nonconvex objectives and constraints. However, we show that by employing polynomial and histogram density estimates, we can introduce robustness with respect to distributional uncertainty sets without making the problem harder. We show that the solution to the distributionally robust problem is the limit of a sequence of tractable semidefinite programming relaxations. We also give finite-sample consistency guarantees for the data-driven uncertainty sets. Finally, we apply our model and solution method in a water network problem.

Author Information

Martin Mevissen (IBM Research)
Emanuele Ragnoli (IBM Research)
Jia Yuan Yu (IBM Research)