# Communication Efficient Distributed Newton Method with Fast Convergence Rates

arXiv: https://arxiv.org/abs/2305.17945 · HTML: https://mlsanity.com/paper/2305.17945/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2023.

## Built on by (most cited first, 4 of 4)

- [Near-Optimal Nonconvex-Strongly-Convex Bilevel Optimization with Fully First-Order Oracles](https://mlsanity.com/paper/2306.14853/) (2023)
- [Second-Order Min-Max Optimization with Lazy Hessians](https://mlsanity.com/paper/2410.09568/) (2024)
- [Incremental Gauss--Newton Methods with Superlinear Convergence Rates](https://mlsanity.com/paper/2407.03195/) (2024)
- [Distributed gradient methods under heavy-tailed communication noise](https://mlsanity.com/paper/2505.24464/) (2025)

## Abstract (arXiv)

We propose a communication and computation efficient second-order method for distributed optimization. For each iteration, our method only requires O(d) communication complexity, where d is the problem dimension. We also provide theoretical analysis to show the proposed method has the similar convergence rate as the classical second-order optimization algorithms. Concretely, our method can find~big(ε, √dLε,big)-second-order stationary points for nonconvex problem by Obig(√dL,ε-3/2big) iterations, where L is the Lipschitz constant of Hessian. Moreover, it enjoys a local superlinear convergence under the strongly-convex assumption. Experiments on both convex and nonconvex problems show that our proposed method performs significantly better than baselines.