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

arXiv: https://arxiv.org/abs/2106.09663 · HTML: https://mlsanity.com/paper/2106.09663/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 1 references that are in the map.
- First posted on arXiv 17 Jun 2021.

## Builds on (most cited first, 1 of 1)

- [PAGE: A Simple and Optimal Probabilistic Gradient Estimator for Nonconvex Optimization](https://mlsanity.com/paper/2008.10898/) (2020)

## Built on by (most cited first, 4 of 4)

- [CANITA: Faster Rates for Distributed Convex Optimization with Communication Compression](https://mlsanity.com/paper/2107.09461/) (2021)
- [FedPAGE: A Fast Local Stochastic Gradient Method for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2108.04755/) (2021)
- [DESTRESS: Computation-Optimal and Communication-Efficient Decentralized Nonconvex Finite-Sum Optimization](https://mlsanity.com/paper/2110.01165/) (2021)
- [Faster Rates for Compressed Federated Learning with Client-Variance Reduction](https://mlsanity.com/paper/2112.13097/) (2021)

## Abstract (arXiv)

In this note, we first recall the nonconvex problem setting and introduce the optimal PAGE algorithm (Li et al., ICML'21). 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.