A Parameter-Free First-Order Algorithm for Non-Convex Optimization with $\tilde{\mkern1mu O}(ε^{-5/3})$ Global Rate
We introduce PF-AGD, the first parameter-free, deterministic, accelerated first-order method to achieve $O(ε^{-5/3}\log(1/ε))$ oracle complexity bound when minimizing sufficiently smooth, non-convex functions; this is the best-known bound for first-order methods on smooth non-convex objectives. Unlike existing methods possessing this rate that require a priori knowledge of smoothness constants, we use an adaptive backtracking scheme and a gradient-based restart mechanism to estimate local curvature. This yields a practical algorithm that matches best-known theoretical rates. Empirically, PF-AGD outperforms the practical variant of AGD-Until-Guilty (Carmon et al., 2017), as well as other p...
| Authors | Sichao Xiong, Sadok Jerad, Coralia Cartis |
|---|---|
| Primary category | math.OC |
| Published | 4 May 2026 |
| Last updated at source | 4 May 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.