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, by leveraging information on the curvature of the problem.

翻译：我们提出了一种分布式拟牛顿（DQN）方法，使一组智能体能够利用聚合目标函数曲率的近似值，局部求解可分离的多智能体优化问题的最优解。每个智能体通过使用其局部目标函数梯度的拟牛顿近似方案，从其局部聚合Hessian估计中计算出下降方向。此外，我们针对等式约束优化提出了一种分布式拟牛顿方法（EC-DQN），其中每个智能体采用类Karush-Kuhn-Tucker更新步骤来计算最优解。在我们的算法中，每个智能体通过对等通信网络与其单跳邻居进行通信，以计算共同解。我们证明了算法收敛到优化问题的平稳点。此外，与现有的分布式一阶和二阶方法相比，我们的算法在良态和病态优化问题的计算时间和通信成本方面均表现出有竞争力的经验收敛性。特别是在病态问题中，通过利用问题的曲率信息，我们的算法在不同连通程度的通信网络中实现了更快的收敛计算时间，同时降低了通信成本。