Federated adversary domain adaptation is a unique distributed minimax training task due to the prevalence of label imbalance among clients, with each client only seeing a subset of the classes of labels required to train a global model. To tackle this problem, we propose a distributed minimax optimizer referred to as FedMM, designed specifically for the federated adversary domain adaptation problem. It works well even in the extreme case where each client has different label classes and some clients only have unsupervised tasks. We prove that FedMM ensures convergence to a stationary point with domain-shifted unsupervised data. On a variety of benchmark datasets, extensive experiments show that FedMM consistently achieves either significant communication savings or significant accuracy improvements over federated optimizers based on the gradient descent ascent (GDA) algorithm. When training from scratch, for example, it outperforms other GDA based federated average methods by around $20\%$ in accuracy over the same communication rounds; and it consistently outperforms when training from pre-trained models with an accuracy improvement from $5.4\%$ to $9\%$ for different networks.

提出了FedMM优化器，它专为联合对抗领域适应问题而设计，在不平衡标签和未监督任务的极端情况下表现良好。实验结果表明，与基于渐变下降算法的联合优化器相比，FedMM可以显著提高模型的准确性，尤其是在有目标类别不同的客户端中。

FedMM: 针对联邦对抗领域自适应的鞍点优化算法