Sufficient Statistics for Team Decision Problems

Abstract:

Team decision problems are a static simplification of decentralized Markov decision problems, and form a fundamental building block of decentralized control problems. An early paper by Radner showed that, in the special case when all random variables are Gaussian and the cost function is quadratic, there exist optimal policies that are linear functions. However, Tsitsiklis and Athans proved that the general case is NP-hard. In classical decision problems, sufficient statistics have many uses: they allow us to compress our measurements without sacrificing performance; they simplify the search for optimal policies; and they often provide useful insight into the structure of the problem. Wu and Lall gave a definition of sufficient statistics for team decision problems, and showed that these statistics are sufficient for optimality, and possess a number of other desirable properties, such as being readily updated when new measurements become available. Lemon and Lall recently defined a related class of weak team sufficient statistics, and showed that these statistics are not only sufficient for optimality, but also necessary for simultaneous optimality with respect to all cost functions. We are currently investigating the relationship between these two classes of sufficient statistics, and determining which desirable properties of team sufficient statistics are shared by weak team sufficient statistics.