Distributionally Robust Optimization with Polynomial Robust Constraints

TL;DR

This paper introduces a Moment-SOS relaxation method for solving distributionally robust optimization problems with polynomial constraints, enabling efficient solutions for both convex and certain nonconvex cases.

Contribution

It develops a novel Moment-SOS relaxation approach for DRO with polynomial constraints, including conditions for global solutions in nonconvex cases.

Findings

Efficient solution method demonstrated through numerical experiments.

Equivalence between SOS-convex DRO and linear conic relaxation.

Applicable to both convex and certain nonconvex DRO problems.

Abstract

This paper studies distributionally robust optimization (DRO) with polynomial robust constraints. We give a Moment-SOS relaxation approach to solve the DRO. This reduces to solving linear conic optimization with semidefinite constraints. When the DRO problem is SOS-convex, we show that it is equivalent to the linear conic relaxation and it can be solved by the Moment-SOS algorithm. For nonconvex cases, we also give concrete conditions such that the DRO can be solved globally. Numerical experiments are given to show the efficiency of the method.