Convergence Analysis of the PAGE Stochastic Algorithm for Weakly Convex Finite-Sum Optimization
This work provides incremental theoretical analysis for optimization algorithms, addressing a specific mathematical framework in machine learning.
The paper tackled the problem of analyzing the convergence of the PAGE stochastic algorithm for weakly convex finite-sum optimization, establishing new convergence rates that improve as the weak convexity parameter decreases.
PAGE, a stochastic algorithm introduced by Li et al. [2021], was designed to find stationary points of averages of smooth nonconvex functions. In this work, we study PAGE in the broad framework of $τ$-weakly convex functions, which provides a continuous interpolation between the general nonconvex $L$-smooth case ($τ= L$) and the convex case ($τ= 0$). We establish new convergence rates for PAGE, showing that its complexity improves as $τ$ decreases.