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