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The non-smooth finite-sum minimization is a fundamental problem in machinelearning. This paper develops a distributed stochastic proximal-gradientalgorithm with random reshuffling to solve the finite-sum minimization overtime-varying multi-agent networks. The objective function is a sum ofdifferentiable convex functions and non-smooth regularization. Each agent inthe network updates local variables with a constant step-size by localinformation and cooperates to seek an optimal solution. We prove that localvariable estimates generated by the proposed algorithm achieve consensus andare attracted to a neighborhood of the optimal solution in expectation with an$\mathcal{O}(\frac{1}{T}+\frac{1}{\sqrt{T}})$ convergence rate, where $T$ isthe total number of iterations. Finally, some comparative simulations areprovided to verify the convergence performance of the proposed algorithm.

Distributed stochastic proximal algorithm with random reshuffling for non-smooth finite-sum optimization