A Short Note of PAGE: Optimal Convergence Rates for Nonconvex Optimization

In this note, we first recall the nonconvex problem setting and introduce the optimal PAGE algorithm (Li et al., 2021). Then we provide a simple and clean convergence analysis of PAGE for achieving optimal convergence rates. Moreover, PAGE and its analysis can be easily adopted and generalized to other works. We hope that this note provides the insights and is helpful for future works. The nonconvex function f has the following two forms: 1. Finite-sum form Now we define the following standard assumptions.