Distributed Distributionally Robust Optimization with Non-Convex Objectives
This work addresses key challenges in distributed DRO for applications like network behavior analysis and risk management, offering an incremental improvement over existing methods.
The paper tackles the problem of distributed distributionally robust optimization (DDRO) with non-convex objectives by proposing the ASPIRE algorithm with EASE and a constrained D-norm uncertainty set, achieving fast convergence, robustness against data heterogeneity and malicious attacks, and a trade-off between robustness and performance in empirical studies on real-world datasets.
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.