Distributed stochastic optimization via correlated scheduling

TL;DR

This paper introduces a distributed stochastic optimization method where users coordinate decisions via correlated pseudorandom sequences to maximize utility under constraints, applicable to sensor networks and similar systems.

Contribution

It presents a novel approach for distributed decision-making using correlated scheduling to achieve optimal utility under constraints.

Findings

Optimality is achieved through correlated user decisions.

An algorithm based on time-varying weights is developed.

The method applies to power-constrained sensor networks.

Abstract

This paper considers a problem where multiple users make repeated decisions based on their own observed events. The events and decisions at each time step determine the values of a utility function and a collection of penalty functions. The goal is to make distributed decisions over time to maximize time average utility subject to time average constraints on the penalties. An example is a collection of power constrained sensor nodes that repeatedly report their own observations to a fusion center. Maximum time average utility is fundamentally reduced because users do not know the events observed by others. Optimality is characterized for this distributed context. It is shown that optimality is achieved by correlating user decisions through a commonly known pseudorandom sequence. An optimal algorithm is developed that chooses pure strategies at each time step based on a set of time-varying weights.