---
title: "Riemannian Stochastic Recursive Momentum Method for non-Convex Optimization"
authors:
  - "Andi Han"
  - "Junbin Gao"
doi: "10.24963/ijcai.2021/345"
url: "https://ijcai.org/proceedings/2021/345"
pdf: "https://ijcai.org/proceedings/2021/0345.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "2505-2511"
track: "Main Track"
keywords:
  - "Machine Learning: Online Learning"
---

# Riemannian Stochastic Recursive Momentum Method for non-Convex Optimization

Andi Han, Junbin Gao

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 2505-2511. DOI: [10.24963/ijcai.2021/345](https://doi.org/10.24963/ijcai.2021/345)

## Abstract

We propose a stochastic recursive momentum method for Riemannian non-convex optimization that achieves a nearly-optimal complexity to find epsilon-approximate solution with one sample. The new algorithm requires one-sample gradient evaluations per iteration and does not require restarting with a large batch gradient, which is commonly used to obtain a faster rate. Extensive experiment results demonstrate the superiority of the proposed algorithm. Extensions to nonsmooth and constrained optimization settings are also discussed.