# A Stochastic Second-Order Proximal Method for Distributed Optimization

arXiv: https://arxiv.org/abs/2211.10591 · HTML: https://mlsanity.com/paper/2211.10591/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2022.

## Built on by (most cited first, 1 of 1)

- [Adaptive pruning-based Newton's method for distributed learning](https://mlsanity.com/paper/2308.10154/) (2023)

## Abstract (arXiv)

In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm, referred to as St-SoPro, incorporates a decentralized second-order approximation into an augmented Lagrangian function, and then randomly samples the local gradients and Hessian matrices of the agents, so that it is computationally and memory-wise efficient, particularly for large-scale optimization problems. We show that for globally restricted strongly convex problems, the expected optimality error of St-SoPro asymptotically drops below an explicit error bound at a linear rate, and the error bound can be arbitrarily small with proper parameter settings. Simulations over real machine learning datasets demonstrate that St-SoPro outperforms several state-of-the-art distributed stochastic first-order methods in terms of convergence speed as well as computation and communication costs.