Walk Proximal Gradient: An Energy-Efficient Algorithm for Consensus Optimization

Decentralized computing is widely used for multiagent systems since it works without a central computing node. In this paper, we develop a first-order algorithm for decentralized consensus optimization that is more energy efficient than the current state-of-the-art. Our algorithm is suitable for application scenarios such as networks of wireless sensors and Internet of Things, where some agents have limited (battery) energy. We call our algorithm walk proximal gradient (WPG), which passes a token through a walk (a succession of nodes) in the graph. The agents that are visited during the walk compute the gradients of their private functions and update the token. We analyze WPG where the walk is the repetition of a Hamiltonian cycle and show that the token converges to the consensual solution faster (in terms of energy consumption) than existing gradient-based decentralized methods. We also generalize the analysis to the non-Hamiltonian graphs. Numerical experiments are presented to validate the energy efficiency of our algorithm.