# Distributed Quasi-Newton Method for Multi-Agent Optimization

arXiv: https://arxiv.org/abs/2402.06778 · HTML: https://mlsanity.com/paper/2402.06778/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2024.

## Built on by (most cited first, 2 of 2)

- [Distributed gradient methods under heavy-tailed communication noise](https://mlsanity.com/paper/2505.24464/) (2025)
- [CoCoL: A Communication Efficient Decentralized Collaborative Method for Multi-Robot Systems](https://mlsanity.com/paper/2508.20898/) (2025)

## Abstract (arXiv)

We present a distributed quasi-Newton (DQN) method, which enables a group of agents to compute an optimal solution of a separable multi-agent optimization problem locally using an approximation of the curvature of the aggregate objective function. Each agent computes a descent direction from its local estimate of the aggregate Hessian, obtained from quasi-Newton approximation schemes using the gradient of its local objective function. Moreover, we introduce a distributed quasi-Newton method for equality-constrained optimization (EC-DQN), where each agent takes Karush-Kuhn-Tucker-like update steps to compute an optimal solution. In our algorithms, each agent communicates with its one-hop neighbors over a peer-to-peer communication network to compute a common solution. We prove convergence of our algorithms to a stationary point of the optimization problem. In addition, we demonstrate the competitive empirical convergence of our algorithm in both well-conditioned and ill-conditioned optimization problems, in terms of the computation time and communication cost incurred by each agent for convergence, compared to existing distributed first-order and second-order methods. Particularly, in ill-conditioned problems, our algorithms achieve a faster computation time for convergence, while requiring a lower communication cost, across a range of communication networks with different degrees of connectedness.