Distributed Learning with Non-Smooth Objective Functions

We develop a new distributed algorithm to solve a learning problem with non-smooth objective functions when data are distributed over a multi-agent network. We employ a zeroth-order method to minimize the associated augmented Lagrangian in the primal domain using the alternating direction method of multipliers (ADMM) to develop the proposed algorithm, named distributed zeroth-order based ADMM (D-ZOA). Unlike most existing algorithms for non-smooth optimization, which rely on calculating subgradients or proximal operators, D-ZOA only requires function values to approximate gradients of the objective function. Convergence of D-ZOA to the centralized solution is confirmed via theoretical analysis and simulation results.