A Parameter-Free First-Order Algorithm for Non-Convex Optimization with $\tilde{\mkern1mu O}(ε^{-5/3})$ Global Rate

• URL: http://arxiv.org/abs/2605.02127v1
• Date: Mon, 04 May 2026 01:17:06 GMT
• Title: A Parameter-Free First-Order Algorithm for Non-Convex Optimization with $\tilde{\mkern1mu O}(ε^{-5/3})$ Global Rate
• Abstract summary: We introduce PF-AGD, the first parameter-free, accelerated first-order method to achieve $O(-5)$ complexity on smooth non-log objectives.
• Score: 0.12744523252873352
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 parameter-free variants, and is a viable alternative to nonlinear conjugate gradient methods.

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