Distributed Algorithms for Composite Optimization: Unified Framework and Convergence Analysis

We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions-the agents' sum-utility-plus nonsmooth (extended-valued) one. propose general unified algorithmic framework for such class problems and provide convergence analysis leveraging the theory operator splitting. Distinguishing features our scheme are: (i) When each agent's functions is strongly convex, algorithm converges at linear rate, whose dependence on network topology decoupled; (ii) objective function (but not convex), similar decoupling as in established coefficient proved sublinear rate. This also reveals role heterogeneity (iii) The can adjust ratio between number communications computations to achieve rate (in terms computations) independent connectivity; (iv) A by-product tuning recommendation several existing (non-accelerated) algorithms yielding provably faster (worst-case) under consideration.