Minimax problems arise in a wide range of important applications including robust adversarial learning and Generative Adversarial Network (GAN) training. Recently, algorithms for minimax problems in the Federated Learning (FL) paradigm have received considerable interest. Existing federated algorithms for general minimax problems require the full aggregation (i.e., aggregation of local model information from all clients) in each training round. Thus, they are inapplicable to an important setting of FL known as the cross-device setting, which involves numerous unreliable mobile/IoT devices. In this paper, we develop the first practical algorithm named CDMA for general minimax problems in the cross-device FL setting. CDMA is based on a Start-Immediately-With-Enough-Responses mechanism, in which the server first signals a subset of clients to perform local computation and then starts to aggregate the local results reported by clients once it receives responses from enough clients in each round. With this mechanism, CDMA is resilient to the low client availability. In addition, CDMA is incorporated with a lightweight global correction in the local update steps of clients, which mitigates the impact of slow network connections. We establish theoretical guarantees of CDMA under different choices of hyperparameters and conduct experiments on AUC maximization, robust adversarial network training, and GAN training tasks. Theoretical and experimental results demonstrate the efficiency of CDMA.

翻译：摘要：极小极大问题广泛存在于鲁棒对抗学习和生成对抗网络（GAN）训练等重要应用中。近年来，联邦学习（FL）范式下的极小极大问题算法受到了广泛关注。现有针对一般极小极大问题的联邦算法需要在每轮训练中进行完整聚合（即聚合所有客户端的局部模型信息），因此无法适用于联邦学习的重要场景——跨设备设置，该场景涉及大量不可靠的移动/物联网设备。本文提出了首个适用于跨设备联邦学习场景中一般极小极大问题的实用算法CDMA。CDMA基于“达到足够响应立即启动”机制，在该机制中，服务器首先指示部分客户端执行本地计算，一旦在每轮中收到足够客户端的响应，便立即开始聚合这些客户端报告的局部结果。该机制使CDMA能够有效应对客户端可用性低的问题。此外，CDMA在客户端的局部更新步骤中集成了轻量级全局校正机制，从而减轻了网络连接缓慢的影响。我们从理论上证明了CDMA在不同超参数选择下的收敛保证，并在AUC最大化、鲁棒对抗网络训练和GAN训练任务上进行了实验。理论与实验结果表明了CDMA的高效性。