Decentralized Stochastic Subgradient-type Methods with Communication Compression for Nonsmooth Nonconvex Optimization

This paper studies decentralized nonsmooth nonconvex optimization when inter-agent communication is compressed. It introduces a general framework covering stochastic subgradient-type methods with unbiased compression and contractive compression combined with error compensation. By connecting consensus-error and averaged iterates to continuous-time differential inclusions, the authors establish global convergence for the methods covered by the framework, including objectives that lack Clarke regularity. The paper also develops compression-based methods using sign-based regularization and gradient-tracking momentum. Preliminary numerical experiments support the theory and illustrate the communication-accuracy trade-off, although the experiments are explicitly described as preliminary.