A One-Sample Decentralized Proximal Algorithm for Non-Convex Stochastic Composite Optimization

Abstract

We focus on decentralized stochastic non-convex optimization, where n agents work together to optimize a composite objective function which is a sum of a smooth term and a non-smooth convex term. To solve this problem, we propose two single-time scale algorithms: Prox-DASA and Prox-DASA-GT. These algorithms can find -stationary points in O(n −1 −2 ) iterations using constant batch sizes (i.e., O(1)). Unlike prior work, our algorithms achieve a comparable complexity result without requiring large batch sizes, more complex per-iteration operations (such as double loops), or stronger assumptions. Our theoretical findings are supported by extensive numerical experiments, which demonstrate the superiority of our algorithms over previous approaches.

Decentralized Gradient-Free Methods for Stochastic Non-smooth Non-convex Optimization

“…Moreover, a substantial volume of literature exists regarding resolving non-convex non-smooth optimization (Di Lorenzo and Scutari 2016;Scutari and Sun 2019;Wang et al 2021;Xin et al 2021;Mancino-Ball et al 2023;Xiao et al 2023;Chen, Garcia, and Shahrampour 2021;Wang et al 2023). However, most existing research require the objective to adhere to a specific structure.…”