Client Sampling for Communication-Efficient Distributed Minimax Optimization

Distributed minimax optimization is essential for robust federated learning, offering resiliency against the variability in data distribution. Most previous works focus only on learning guarantees and convergence analysis, without explicit consideration of the communication delay, which can be crucial in practical systems. In this work, we consider the problem of communication-efficient distributed minimax optimization via judicious client sampling, proposing an algorithm termed CE-MINIMAX, which takes into consideration both the training convergence performance and the communication time per training round. We derive convergence bounds for CE − MINIMAX under both convex and non-convex loss functions, which we then use to design the client sampling probabilities in joint consideration of the communication time. We conduct numerical experiments with canonical classification datasets to demonstrate that CE − MINIMAX can achieve higher worst-case test accuracy under substantially reduced communication time, compared with state-of-the-art client sampling schemes for distributed minimax optimization.