Network optimization with heuristic rational agents

We study a distributed model for optimizing a sum of convex objective functions corresponding to agents in the network. At random times, agents execute actions based on heuristic rational rules considering only local information. Heuristic rational rules are probabilistic and their expectation yields the actual optimal action. Under heuristic rational rule iterations, it is shown that global network cost comes within a close vicinity of the optimal value infinitely often with probability 1. Furthermore, an exponential bound on probability of deviating from vicinity of the optimal value is derived. We exemplify heuristic rational behavior on estimation of a random field using a wireless sensor network.