Distributed Quasi-Newton Method for Multi-Agent Optimization
<|reference_start|>Distributed Quasi-Newton Method for Multi-Agent Optimization: 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.<|reference_end|>
@article{shorinwa2024distributed,
    title={Distributed Quasi-Newton Method for Multi-Agent Optimization},
    author={Ola Shorinwa and Mac Schwager},
    journal={arXiv preprint arXiv:2402.06778},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.06778},
    primaryClass={math.OC cs.MA cs.SY eess.SY}
}