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.

翻译：(dRO) 现有DRO技术面临三大挑战:(1) 如何在分布式环境中应对分布式强势更新;(2) 如何有效利用先前的分布式优化优化(DRO) ;(3) 如何根据不同情景适当调整稳健度;(3) 如何根据不同的情景适当调整稳健度;为此目的,我们提议采用一个非同步分布式算法,名为“Asynchronous SlooP ExplentiveIve gRadient proEction (ASPIRI)” 算法,与“EASE” 模拟主动SET 方法(EASE)一起广泛应用,以解决分布式强势优化问题。此外,正在开发一套新的不确定性,即受限制的D-Norm不确定性集,以有效地利用先前分布式的稳健和灵活控制稳健度。最后,我们提出的理论分析表明,拟议的算法将保证趋同一致,而且它具有高度的稳定性,同时也分析其快速趋同性。