Trading off Communication Cost and Optimization Performance in Decentralized Multi-Task Optimization

In sensor networks or other multi-agent systems, agents often need to make personalized decisions through cooperation, which can be formulated as a decentralized multi-task optimization problem. This paper investigates how to achieve the trade-off between final optimization accuracy and communication cost when solving such problems. We focus on a decentralized optimization problem where the objective is an aggregate sum of local objective functions, regularized by a general quadratic term. Our approach is to find a new quadratic regularized term that approximates the original, guided by which we develop the optimization framework that characterizes both the optimization performance and the associated communication cost. Our framework can handle the case when multi-hop communication is necessary and we further propose leveraging the “compute-and-forward” technique to enhance communication efficiency. We then present an efficient solution method for the proposed problem. Simulation results demonstrate that the “compute-andforward” scheme offers a superior trade-off in comparison to traditional multi-hop communication and validate the effectiveness of the proposed algorithm.