Distributed Network Optimization With Heuristic Rational Agents

A network of distributed agents wants to minimize a global cost given by a sum of local terms involving nonlinear convex functions of self and neighboring variables. Agents update their variables at random times by observing the values of neighboring agents and applying a random heuristic rule intent on minimizing the local cost with respect to their own variables. The heuristic rules are rational in that their average result is the actual optimal action with respect to the given values of neighboring variables. By identifying heuristic rational optimization with stochastic coordinate descent, it is shown that all agents visit a neighborhood of the optimal cost infinitely often with probability 1. An exponential probability bound on the worst deviation from optimality between visits to near optimal operating points is also derived. Commonly used models of consensus and opinion propagation in social networks, Markov random field estimation in wireless sensor networks, and cohesive foraging of animal herds are cast in the language of heuristic rational optimization. Numerical simulations for these three examples are presented to corroborate analytical results.