Distributed Stochastic Optimization via Correlated Scheduling
Abstract: This paper considers a problem where multiple devices 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 sensors that repeatedly report their own observations to a fusion center. Maximum time-average utility is fundamentally reduced because devices do not know the events observed by others. Optimality is characterized for this distributed context. It is shown that optimality is achieved by correlating device decisions through a commonly known pseudo-random sequence. An optimal algorithm is developed that chooses pure strategies at each time-step based on a set of time-varying weights.