# Cooperative data-driven distributionally robust optimization

arXiv: https://arxiv.org/abs/1711.04839 · HTML: https://mlsanity.com/paper/1711.04839/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2017.

## Built on by (most cited first, 5 of 5)

- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [FDR-SVM: A Federated Distributionally Robust Support Vector Machine via a Mixture of Wasserstein Balls Ambiguity Set](https://mlsanity.com/paper/2410.03877/) (2024)
- [A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification](https://mlsanity.com/paper/2608.29789/) (2026)
- [Distributionally Robust Federated Learning with Multi-Source Data](https://mlsanity.com/paper/2609.20501/) (2026)

## Abstract (arXiv)

This paper studies a class of multiagent stochastic optimization problems where the objective is to minimize the expected value of a function which depends on a random variable. The probability distribution of the random variable is unknown to the agents, so each one gathers samples of it. The agents aim to cooperatively find, using their data, a solution to the optimization problem with guaranteed out-of-sample performance. The approach is to formulate a data-driven distributionally robust optimization problem using Wasserstein ambiguity sets, which turns out to be equivalent to a convex program. We reformulate the latter as a distributed optimization problem and identify a convex-concave augmented Lagrangian function whose saddle points are in correspondence with the optimizers provided a min-max interchangeability criteria is met. Our distributed algorithm design then consists of the saddle-point dynamics associated to the augmented Lagrangian. We formally establish that the trajectories of the dynamics converge asymptotically to a saddle point and hence an optimizer of the problem. Finally, we provide a class of functions that meet the min-max interchangeability criteria. Simulations illustrate our results.