Rethinking Distributed Average Consensus for Wireless Networks: A Low-Cost Approach to Broadcast Probability Optimization

This letter rethinks the probabilistic broadcast gossip scheme to achieve fast distributed average consensus in wireless networks. The consensus attainment in this scheme is heavily influenced by the broadcast probability of each node, which directly affects the convergence rate. To reduce communication costs for achieving consensus, we formulate an optimization problem to determine the optimal broadcast probability for each node. This problem involves a challenging nonconvex spectral radius term in the objective function. To address this challenge, we introduce an enhanced majorization-minimization-based approach that leverages a novel surrogate function to effectively upper bound the spectral radius function. Simulation results show that the proposed method provides substantial performance improvements over existing heuristic methods for broadcast probability optimization.