Distributed Stochastic Optimization via Correlated Scheduling

This talk considers two distributed optimization problems.  In the first problem, 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 a 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 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.

 

The second problem treats multiple systems that perform tasks over different timescales, such as a collection of smart devices that perform data processing and communication using separate chips. The resulting optimization problem is non-convex and has fractional terms with different denominators.  An asynchronous drift-plus-penalty ratio algorithm is developed for optimality.