We develop two new algorithms, called, FedDR and asyncFedDR, for solving a fundamental nonconvex composite optimization problem in federated learning. Our algorithms rely on a novel combination between a nonconvex Douglas-Rachford splitting method, randomized block-coordinate strategies, and asynchronous implementation. They can also handle convex regularizers. Unlike recent methods in the literature, e.g., FedSplit and FedPD, our algorithms update only a subset of users at each communication round, and possibly in an asynchronous manner, making them more practical. These new algorithms also achieve communication efficiency and more importantly can handle statistical and system heterogeneity, which are the two main challenges in federated learning. Our convergence analysis shows that the new algorithms match the communication complexity lower bound up to a constant factor under standard assumptions. Our numerical experiments illustrate the advantages of our methods compared to existing ones on several datasets.
翻译:我们开发了两种新的算法,称为FedDR和AsyncFedDR,用于解决联合学习中一个基本的非Convex复合优化问题。我们的算法依赖于非Convex Douglas-Rachford分解法、随机的区块协调战略和非同步执行之间的新组合。它们也可以处理 convex正规化者。与文献中最近的方法不同,例如FedSplit和FedPD,我们的算法只更新每个通信周期的用户组,可能以不同步的方式更新,使其更加实用。这些新的算法还实现了通信效率,更重要的是能够处理统计和系统差异性,这是混合学习的两大挑战。我们的趋同分析表明,新的算法将通信复杂性与标准假设下的固定因素相匹配。我们的数字实验显示了我们方法与几个数据集的现有方法相比的优势。