Linear Convergence of Distributed Compressed Optimization with Equality Constraints
Zihao Ren, Lei Wang, Zhengguang Wu, Guodong Shi
TL;DR
This work tackles distributed strongly convex optimization with equality constraints under spatio-temporal compressed communication. It develops two ST-compressed saddle-point algorithms—CDC-DE for distributed linear equalities and CDC-CE for coupled equalities—each augmented with distributed filters to manage communication-induced errors. Both algorithms provably achieve linear convergence under appropriate compressor gains and stepsizes, validated by numerical simulations. The results demonstrate that communication compression can be integrated with constraint-satisfying distributed optimization without sacrificing convergence speed, enabling scalable, bandwidth-efficient implementations in networked systems.
Abstract
In this paper, the distributed strongly convex optimization problem is studied with spatio-temporal compressed communication and equality constraints. For the case where each agent holds an distributed local equality constraint, a distributed saddle-point algorithm is proposed by employing distributed filters to derive errors of the transmitted states for spatio-temporal compression purposes. It is shown that the resulting distributed compressed algorithm achieves linear convergence. Furthermore, the algorithm is generalized to the case where each agent holds a portion of the global equality constraint, i.e., the constraints across agents are coupled. By introducing an additional design freedom, the global equality constraint is shown to be equivalent to the one where each agent holds an equality constraint, for which the proposed distributed compressed saddle-point algorithm can be adapted to achieve linear convergence. Numerical simulations are adopted to validate the effectiveness of the proposed algorithms.