This paper proposes a stochastic proximal point method to solve a stochastic convex composite optimization problem. High probability results in stochastic optimization typically hinge on restrictive assumptions on the stochastic gradient noise, for example, sub-Gaussian distributions. Assuming only weak conditions such as bounded variance of the stochastic gradient, this paper establishes a low sample complexity to obtain a high probability guarantee on the convergence of the proposed method. Additionally, a notable aspect of this work is the development of a subroutine to solve the proximal subproblem, which also serves as a novel technique for variance reduction.

翻译：本文提出一种随机近端点方法，用于求解随机凸复合优化问题。随机优化中的高概率结果通常依赖于对随机梯度噪声的严格假设（例如次高斯分布）。本文仅假设随机梯度方差有界等弱条件，即为所提方法的收敛性建立了一种低样本复杂度的高概率保证。此外，本工作的一个显著特点是开发了用于求解近点子问题的子程序，该子程序同时也作为一种新颖的方差缩减技术。