PAGE算法在弱凸优化中收敛更快，τ越小效果越好。
Convergence Analysis of the ProbAbilistic Gradient Estimator Algorithm for Weakly Convex Finite-Sum Optimization
- 将PAGE算法扩展至τ-弱凸函数框架
- 证明τ越小收敛速度越快，复杂度降低
- 适用于非凸到凸之间的连续优化场景
ProbAbilistic Gradient Estimator算法（PAGE）由Li等人于2021年提出，旨在寻找光滑非凸函数之和的驻点。本文在τ-弱凸函数的广泛框架下研究PAGE算法，实现了从一般非凸L-光滑情形（τ = L）到凸情形（τ = 0）的连续插值。我们建立了新的收敛速率，表明随着τ减小，算法复杂度显著改善。
原文摘要 · Abstract (English)
The ProbAbilistic Gradient Estimator algorithm (PAGE), a stochastic algorithm introduced by Li et al. in 2021, was designed to find stationary points for the average of smooth nonconvex functions. In this work, we study PAGE within the broad framework of $τ$-weakly convex functions, providing a continuous interpolation between the general nonconvex $L$-smooth regime ($τ=L$) and the convex regime ($τ=0$). We establish new convergence rates for PAGE, showing that its complexity improves as $τ$ decreases.
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