Decentralized ADMM with compressed and event-triggered communication

This paper considers the decentralized optimization problem, where agents in a network cooperate to minimize the sum of their local objective functions by communication and local computation. We propose a decentralized second-order communication-efficient algorithm called communication-censored and communication-compressed quadratically approximated alternating direction method of multipliers (ADMM), termed as CC-DQM, by combining event-triggered communication with compressed communication. In CC-DQM, agents are allowed to transmit the compressed message only when the current primal variables have changed greatly compared to its last estimate. Moreover, to relieve the computation cost, the update of Hessian is also scheduled by the trigger condition. Theoretical analysis shows that the proposed algorithm can still maintain an exact linear convergence, despite the existence of compression error and intermittent communication, if the local objective functions are strongly convex and smooth. Finally, numerical experiments demonstrate its satisfactory communication efficiency.(C) 2023 Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes a decentralized second-order communication-efficient algorithm called CC-DQM, which combines event-triggered communication with compressed communication to solve the decentralized optimization problem. The theoretical analysis shows that the proposed algorithm can achieve exact linear convergence even with compression error and intermittent communication if the local objective functions are strongly convex and smooth. Numerical experiments demonstrate its satisfactory communication efficiency.