BEER: Fast $O(1/T)$ Rate for Decentralized Nonconvex Optimization with Communication Compression

Abstract

Communication efficiency has been widely recognized as the bottleneck for large-scale decentralized machine learning applications in multi-agent or federated environments. To tackle the communication bottleneck, there have been many efforts to design communication-compressed algorithms for decentralized nonconvex optimization, where the clients are only allowed to communicate a small amount of quantized information (aka bits) with their neighbors over a predefined graph topology. Despite significant efforts, the state-of-the-art algorithm in the nonconvex setting still suffers from a slower rate of convergence O((G/T ) 2/3 ) compared with their uncompressed counterpart, where G measures the data heterogeneity across different clients, and T is the number of communication rounds. This paper proposes BEER, which adopts communication compression with gradient tracking, and shows it converges at a faster rate of O(1/T ). This significantly improves over the state-of-the-art rate, by matching the rate without compression even under arbitrary data heterogeneity. Numerical experiments are also provided to corroborate our theory and confirm the practical superiority of BEER in the data heterogeneous regime.

CEDAS: A Compressed Decentralized Stochastic Gradient Method with Improved Convergence

“…(2) primal-dual like methods [22,17,15,14,54,51]; (3) gradient tracking based algorithms [20,55,37,50,47].…”

SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression

“…Therefore, it is very important to design FL algorithms to reduce the overall communication cost, which takes into account both the number of communication rounds and the cost per communication round for reaching a desired accuracy. With these two quantities in mind, there are two principal approaches for communication-efficient FL: 1) local methods, where in each communication round, clients run multiple local update steps before communicating with the server, in the hope of reducing the number of communication rounds, e.g., [47,43,36,24,35,61,51,2,67,50,49,42]; 2) compression methods, where clients send compressed communication message to the server, in the hope of reducing the cost per communication round, e.g., [4,37,60,28,34,48,52,25,53,19,41,68]. While both categories have garnered significant attention in recent years, we will focus on the second approach based on communication compression to enhance communication efficiency.…”