# Riemannian stochastic recursive momentum method for non-convex optimization

arXiv: https://arxiv.org/abs/2008.04555 · HTML: https://mlsanity.com/paper/2008.04555/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2020.

## Built on by (most cited first, 7 of 7)

- [Differentially private Riemannian optimization](https://mlsanity.com/paper/2205.09494/) (2022)
- [Zeroth-order Riemannian Averaging Stochastic Approximation Algorithms](https://mlsanity.com/paper/2309.14506/) (2023)
- [Riemannian accelerated gradient methods via extrapolation](https://mlsanity.com/paper/2208.06619/) (2022)
- [A Framework for Bilevel Optimization on Riemannian Manifolds](https://mlsanity.com/paper/2402.03883/) (2024)
- [Efficient Optimization with Orthogonality Constraint: a Randomized Riemannian Submanifold Method](https://mlsanity.com/paper/2505.12378/) (2025)
- [Rieoptax: Riemannian Optimization in JAX](https://mlsanity.com/paper/2210.04840/) (2022)
- [A Unified Momentum-based Paradigm of Decentralized SGD for Non-Convex Models and Heterogeneous Data](https://mlsanity.com/paper/2303.00179/) (2023)

## Abstract (arXiv)

We propose a stochastic recursive momentum method for Riemannian non-convex optimization that achieves a near-optimal complexity of tildeO(ε-3) to find ε-approximate solution with one sample. That is, our method requires O(1) gradient evaluations per iteration and does not require restarting with a large batch gradient, which is commonly used to obtain the faster rate. Extensive experiment results demonstrate the superiority of our proposed algorithm.