Distributionally Robust Optimization with Moment Ambiguity Sets
arXiv:2103.12315
Abstract
This paper studies distributionally robust optimization (DRO) when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomials in decision variables. We reformulate the DRO with equivalent moment conic constraints. Under some general assumptions, we prove the DRO is equivalent to a linear optimization problem with moment and psd polynomial cones. A Moment-SOS relaxation method is proposed to solve it. Its asymptotic and finite convergence are shown under certain assumptions. Numerical examples are presented to show how to solve DRO problems.
arXiv comment26 pages
References in corpus (7)
- Agnostic Federated Learning
- Truncated K-moment problems in several variables
- The A-truncated K-moment problem
- Distributionally robust polynomial chance-constraints under mixture ambiguity sets
- Efficient Algorithms for Distributionally Robust Stochastic Optimization with Discrete Scenario Support
- A Stochastic Subgradient Method for Distributionally Robust Non-Convex Learning
- Learning Diagonal Gaussian Mixture Models and Incomplete Tensor Decompositions