# Catalyst Acceleration for Gradient-Based Non-Convex Optimization

arXiv: https://arxiv.org/abs/1703.10993 · HTML: https://mlsanity.com/paper/1703.10993/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2017.

## Built on by (most cited first, 2 of 2)

- [RECAPP: Crafting a More Efficient Catalyst for Convex Optimization](https://mlsanity.com/paper/2206.08627/) (2022)
- [On Acceleration of Gradient-Based Empirical Risk Minimization using Local Polynomial Regression](https://mlsanity.com/paper/2204.07702/) (2022)

## Abstract (arXiv)

We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed approach allows one to use them on weakly convex objectives, which covers a large class of non-convex functions typically appearing in machine learning and signal processing. In general, the scheme is guaranteed to produce a stationary point with a worst-case efficiency typical of first-order methods, and when the objective turns out to be convex, it automatically accelerates in the sense of Nesterov and achieves near-optimal convergence rate in function values. These properties are achieved without assuming any knowledge about the convexity of the objective, by automatically adapting to the unknown weak convexity constant. We conclude the paper by showing promising experimental results obtained by applying our approach to incremental algorithms such as SVRG and SAGA for sparse matrix factorization and for learning neural networks.