We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting SPP updates are solved using an inexact semismooth Newton framework. We establish detailed convergence results that take the inexactness of the SPP steps into account and that are in accordance with existing convergence guarantees of (proximal) stochastic variance-reduced gradient methods. Numerical experiments show that the proposed algorithm competes favorably with other state-of-the-art methods and achieves higher robustness with respect to the step size selection.

翻译：我们针对一类弱凸复合优化问题，提出了一种可实现的随机近端点(SPP)方法。所提出的随机近端点算法引入了方差缩减机制，并通过非精确半光滑牛顿框架求解生成的SPP更新步骤。我们建立了考虑SPP步骤非精确性的详细收敛结果，且该结果与现有（近端）随机方差缩减梯度方法的收敛性保证一致。数值实验表明，所提出算法与其他最先进方法相比具有竞争力，并在步长选择方面展现出更高的鲁棒性。