标题： 联邦分布鲁棒优化与非凸目标：算法与分析 显示英文标题

标题： Federated Distributionally Robust Optimization with Non-Convex Objectives: Algorithm and Analysis

摘要： 分布鲁棒优化（DRO），旨在找到一种最优决策，以最小化概率分布的模糊集中的最坏情况成本，在各种应用中得到了广泛应用，例如，网络行为分析、风险管理等。 然而，现有的DRO技术面临三个关键挑战：1）如何处理分布式环境中的异步更新；2）如何有效利用先验分布；3）如何根据不同的场景适当调整鲁棒性的程度。 为此，我们提出了一种异步分布式算法，名为异步单循环交替梯度投影（ASPIRE）算法，结合迭代主动集方法（EASE），以解决联邦分布鲁棒优化（FDRO）问题。 此外，开发了一种新的不确定性集，即约束D范数不确定性集，以有效利用先验分布并灵活控制鲁棒性的程度。 最后，我们的理论分析阐明了所提出的算法保证收敛，同时也分析了迭代复杂度。 在真实数据集上的大量实验研究证明，所提出的方法不仅可以实现快速收敛，还能在数据异质性和恶意攻击下保持鲁棒性，同时在鲁棒性与性能之间进行权衡。 显示英文摘要

摘要： 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 federated distributionally robust optimization (FDRO) 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.