Reaching Bayesian consensus in cognitive systems by decision exchanges

We consider the problem of distributed Bayesian hypothesis testing on a set of time invariant hypotheses in a cognitive system of cooperative agents. Each agent in the system obtains one set of private observations and then at every time slot two randomly selected agents repeatedly exchange their decisions and update their beliefs. We propose a method that allows the agents to reach an optimal local consensus by just exchanging decisions. It can be shown that with this strategy, all agents in the system can achieve a consensus in decision, which is also the global optimal decision held by a fictitious fusion center. We provide performance and convergence analysis of the proposed method as well as simulation results that demonstrate its asymptotical properties.