# Parameter-free accelerated gradient descent for nonconvex minimization

arXiv: https://arxiv.org/abs/2212.06410 · HTML: https://mlsanity.com/paper/2212.06410/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2022.

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

- [Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient](https://mlsanity.com/paper/2301.04431/) (2023)
- [Improved Complexity for Smooth Nonconvex Optimization: A Two-Level Online Learning Approach with Quasi-Newton Methods](https://mlsanity.com/paper/2412.02175/) (2024)
- [Improving Online-to-Nonconvex Conversion for Smooth Optimization via Double Optimism](https://mlsanity.com/paper/2510.03167/) (2025)
- [Stochastic Generative Plug-and-Play Priors](https://mlsanity.com/paper/2604.03603/) (2026)
- [Sharp First-Order Lower Bounds for Higher-Order Smooth Nonconvex Optimization](https://mlsanity.com/paper/2606.05438/) (2026)
- [Newton-CG methods for nonconvex unconstrained optimization with H"older continuous Hessian](https://mlsanity.com/paper/2311.13094/) (2023)
- [A Parameter-Free First-Order Algorithm for Non-Convex Optimization with tildemkern1mu O(ε-5/3) Global Rate](https://mlsanity.com/paper/2605.02127/) (2026)

## Abstract (arXiv)

We propose a new first-order method for minimizing nonconvex functions with a Lipschitz continuous gradient and Hessian. The proposed method is an accelerated gradient descent with two restart mechanisms and finds a solution where the gradient norm is less than ε in O(ε-7/4) function and gradient evaluations. Unlike existing first-order methods with similar complexity bounds, our algorithm is parameter-free because it requires no prior knowledge of problem-dependent parameters, e.g., the Lipschitz constants and the target accuracy ε. The main challenge in achieving this advantage is estimating the Lipschitz constant of the Hessian using only first-order information. To this end, we develop a new Hessian-free analysis based on two technical inequalities: a Jensen-type inequality for gradients and an error bound for the trapezoidal rule. Several numerical results illustrate that the proposed method performs comparably to existing algorithms with similar complexity bounds, even without parameter tuning.