Distributed Quasi-Newton Method for Multi-Agent Optimization
Ola Shorinwa, Mac Schwager · IEEE Transactions on Signal Processing · 2024
We present adistributed quasi-Newton(DQN) method, which enables a group of agents to compute an optimal solution of aseparable multi-agentoptimization 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 forequality-constrainedoptimization (EC-DQN), where each agent takesKarush-Kuhn-Tucker-like update steps to compute an optimal solution. In our algorithms, each agent communicates with its one-hop neighbors over apeer-to-peercommunication 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 bothwell-conditionedandill-conditionedoptimization problems, compared to existing distributedfirst-orderandsecond-ordermethods. Particularly, inill-conditionedproblems, 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.