A One-Sample Decentralized Proximal Algorithm for Non-Convex Stochastic Composite Optimization
This work addresses efficient decentralized optimization for multi-agent systems, offering a practical improvement over existing approaches by reducing computational overhead.
The paper tackles decentralized stochastic non-convex composite optimization by proposing two single-time scale algorithms, Prox-DASA and Prox-DASA-GT, which achieve ε-stationary points in O(n^{-1}ε^{-2}) iterations with constant batch sizes, outperforming prior methods that require larger batches or more complex operations.
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 $ε$-stationary points in $\mathcal{O}(n^{-1}ε^{-2})$ iterations using constant batch sizes (i.e., $\mathcal{O}(1)$). Unlike prior work, our algorithms achieve comparable complexity 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. Our code is available at https://github.com/xuxingc/ProxDASA.