Distributed Distributionally Robust Optimization with Non-Convex Objectives

TL;DR

This paper introduces ASPIRE, an asynchronous distributed algorithm for distributionally robust optimization that effectively leverages prior distributions, adapts robustness levels, and guarantees convergence, demonstrated through empirical studies.

Contribution

The paper proposes a novel asynchronous distributed algorithm with a new uncertainty set for improved robustness and convergence in distributionally robust optimization.

Findings

Achieves fast convergence in empirical tests

Remains robust against data heterogeneity and attacks

Balances robustness and performance effectively

Abstract

Distributionally Robust Optimization (DRO), which aims to find an optimal decision that minimizes the worst case cost over the ambiguity set of probability distribution, has been widely applied in diverse applications, e.g., network behavior analysis, risk management, etc. However, existing DRO techniques face three key challenges: 1) how to deal with the asynchronous updating in a distributed environment; 2) how to leverage the prior distribution effectively; 3) how to properly adjust the degree of robustness according to different scenarios. To this end, we propose an asynchronous distributed algorithm, named Asynchronous Single-looP alternatIve gRadient projEction (ASPIRE) algorithm with the itErative Active SEt method (EASE) to tackle the distributed distributionally robust optimization (DDRO) problem. Furthermore, a new uncertainty set, i.e., constrained D-norm uncertainty set, is developed to effectively leverage the prior distribution and flexibly control the degree of robustness. Finally, our theoretical analysis elucidates that the proposed algorithm is guaranteed to converge and the iteration complexity is also analyzed. Extensive empirical studies on real-world datasets demonstrate that the proposed method can not only achieve fast convergence, and remain robust against data heterogeneity as well as malicious attacks, but also tradeoff robustness with performance.