A unified mini-batch stochastic accelerated method for nonconvex stochastic programming

This paper studies a class of nonconvex stochastic optimization problems involving simple nonsmooth terms, which commonly arise in machine learning and signal processing applications. We propose a unified mini-batch stochastic accelerated (UMSA) algorithm that handles both convex and nonconvex settings within a single framework. The algorithm achieves the known optimal stochastic first-order oracle ( $$\mathcal {SFO}$$ SFO ) complexity order $$\mathcal{{O}}(\frac{1}{\epsilon ^2})$$ O ( 1 ϵ 2 ) in both cases, and exhibits greater flexibility in parameter selection compared to existing methods. Notably, the proposed UMSA algorithm subsumes several existing algorithms as special cases, offering a unifying perspective on nonsmooth optimization. We provide detailed convergence analysis for both nonconvex and convex scenarios, and show that UMSA is theoretically efficient and practically versatile. Numerical experiments on a nonconvex sparse support vector machine problem validate both the effectiveness and computational efficiency of the proposed UMSA algorithm.