Convergence rates for cooperation in heterogeneous populations

We consider the problem of cooperative distributed estimation within a network of heterogeneous agents. In particular, we study the situation where each agent observes an independent stream of Bernoulli random variables, and the goal is for each to determine its own Bernoulli parameter. The agents of this population can be categorized into a small number of subgroups, where within each group the agents all have identical Bernoulli parameters. For a distributed algorithm based on consensus strategies, we examine the rate at which the agent's estimates converge to the correct values. We show that the expected squared error decreases nearly as fast as centralized ML estimation in a homogeneous population. In a heterogeneous population, we derive an approximation to the expected squared error, as a function of the number of observations. Finally, we present simulation results that compare the predicted expected squared error to that observed in the simulations.