# Distributionally Robust Optimization with Moment Ambiguity Sets

arXiv: https://arxiv.org/abs/2103.12315 · HTML: https://mlsanity.com/paper/2103.12315/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2021.

## Built on by (most cited first, 2 of 2)

- [Global Optimisation of Black-Box Functions with Generative Models in the Wasserstein Space](https://mlsanity.com/paper/2407.11917/) (2024)
- [Robust Metaheuristics under Uncertainty for Berth Allocation and Quay Crane Assignment: A Review](https://mlsanity.com/paper/2608.19214/) (2026)

## Abstract (arXiv)

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.