Distributed stochastic proximal algorithm with random reshuffling for non-smooth finite-sum optimization
It addresses distributed optimization for machine learning tasks with non-smooth regularization, but is incremental as it builds on existing stochastic and proximal methods.
This paper tackles the problem of non-smooth finite-sum optimization in distributed multi-agent networks by developing a stochastic proximal-gradient algorithm with random reshuffling, achieving an expected convergence rate of O(1/T + 1/√T) to a neighborhood of the optimal solution.
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.