Communication-Efficient Decentralized Optimization via Double-Communication Symmetric ADMM

This paper focuses on decentralized composite optimization over networks without a central coordinator. We propose a novel decentralized symmetric ADMM algorithm that incorporates multiple communication rounds within each iteration, derived from a new constraint formulation that enables information exchange beyond immediate neighbors. While increasing per-iteration communication, our approach significantly reduces the total number of iterations and overall com- munication cost. We further design optimal communication rules that minimize the number of rounds and variables transmitted per iteration. The proposed algorithm is shown to achieve linear convergence under standard and relatively weak assumptions (e.g., metric subregularity). Extensive experiments on regression and classification tasks validate the theoretical results and demonstrate superior performance compared to existing decentralized optimization methods.