论文标题
牛顿的半齿随机近端算法，降低了差异
A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction
论文作者
论文摘要
我们为一类弱凸的复合优化问题开发了可实现的随机近端（SPP）方法。所提出的随机近端算法结合了降低方差机制，并使用不精确的半齿牛顿框架来求解所得的SPP更新。我们建立了详细的收敛结果，以考虑SPP步骤的不确定性，并且根据（近端）随机方差减少梯度方法的现有收敛保证。数值实验表明，所提出的算法与其他最先进的方法竞争有利，并且相对于步长选择，可以实现更高的鲁棒性。
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.
