Communication-Efficient Nonconvex Federated Learning With Error Feedback for Uplink and Downlink

Facing large-scale online learning, the reliance on sophisticated model architectures often leads to nonconvex distributed optimization, which is more challenging than convex problems. Online recruited workers, such as mobile phone, laptop, and desktop computers, often have narrower uplink bandwidths than downlink. In this article, we propose two communication-efficient nonconvex federated learning algorithms with error feedback 2021 (EF21) and lazily aggregated gradient (LAG) for adapting uplink and downlink communications. EF21 is a new and theoretically better EF, which consistently and substantially outperforms vanilla EF in practice. LAG is a gradient filtration technique for adapting communication. For reducing communication costs of uplink, we design an effective LAG rule and then give EF21 with LAG (EF-LAG) algorithm, which combines EF21 and our LAG rule. We also present a bidirectional EF-LAG (BiEF-LAG) algorithm for reducing uplink and downlink communication costs. Theoretically, our proposed algorithms enjoy the same fast convergence rate $\mathcal{O}(1/T)$ as gradient descent (GD) for smooth nonconvex learning. That is, our algorithms greatly reduce communication costs without sacrificing the quality of learning. Numerical experiments on both synthetic data and deep learning benchmarks show significant empirical superiority of our algorithms in communication.