Professor Jinde Cao and his team at the School of Mathematics, Southeast University, have achieved significant progress in the field of distributed optimization and learning. Their cutting-edge research, titled "Decentralized Inexact Proximal Gradient Method With Network-Independent Stepsizes for Convex Composite Optimization," has been officially published in the IEEE Transactions on Signal Processing, which stands as one of the leading academic journals in signal processing, sponsored by the IEEE Signal Processing Society. Professor Jinde Cao serves as the corresponding author, and the first authorship is attributed to Luyao Guo, Professor Cao's current Ph.D. student.
In this paper, a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks is proposed. The local loss function in these problems contains both smooth and nonsmooth terms. The proposed algorithm uses uncoordinated network-independent constant stepsizes and only needs to approximately solve a sequence of proximal mappings, which is advantageous for solving decentralized composite optimization problems where the proximal mappings of the nonsmooth loss functions may not have analytical solutions. For the general convex case, the authors proved an O(1/k) convergence rate of the proposed algorithm, which can be improved to o(1/k) if the proximal mappings are solved exactly. Furthermore, with metric subregularity, they established a linear convergence rate for the proposed algorithm. Numerical experiments demonstrate the efficiency of the algorithm.
Full access of the paper is available at https://ieeexplore.ieee.org/document/10056981
