# Problem-Parameter-Free Decentralized Nonconvex Stochastic Optimization

arXiv: https://arxiv.org/abs/2402.08821 · HTML: https://mlsanity.com/paper/2402.08821/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2024.

## Built on by (most cited first, 5 of 5)

- [Federated Learning on Riemannian Manifolds: A Gradient-Free Projection-Based Approach](https://mlsanity.com/paper/2507.22855/) (2025)
- [Near-Optimal Decentralized Stochastic Nonconvex Optimization with Heavy-Tailed Noise](https://mlsanity.com/paper/2601.11435/) (2026)
- [Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum](https://mlsanity.com/paper/2504.12742/) (2025)
- [Decentralized Stochastic Nonconvex Optimization under the (L0,L1)-Smoothness](https://mlsanity.com/paper/2509.08726/) (2025)
- [Adaptive Decentralized Composite Optimization via Three-Operator Splitting](https://mlsanity.com/paper/2602.17545/) (2026)

## Abstract (arXiv)

Existing decentralized algorithms usually require knowledge of problem parameters for updating local iterates. For example, the hyperparameters (such as learning rate) usually require the knowledge of Lipschitz constant of the global gradient or topological information of the communication networks, which are usually not accessible in practice. In this paper, we propose D-NASA, the first algorithm for decentralized nonconvex stochastic optimization that requires no prior knowledge of any problem parameters. We show that D-NASA has the optimal rate of convergence for nonconvex objectives under very mild conditions and enjoys the linear-speedup effect, i.e. the computation becomes faster as the number of nodes in the system increases. Extensive numerical experiments are conducted to support our findings.