Ergodic Theory of Decisions Under Partial Information

Princeton University, Princeton NJ

Investigators

Abstract

This project is concerned with sequential decision problems under partial information. In such problems, decisions must be made sequentially in time. The decision maker has access to an observed component of an ergodic Markov process, but the cost of her decisions is determined also by the unobserved part of the process. The decision maker aims to minimize the long time average cost by the choice of a strategy that is adapted to the filtration generated by the observations only. The goal of the project is to characterize the fundamental properties of optimal decisions, such as pathwise optimality and ergodic theorems, and to investigate certain sub-optimal decision algorithms which can be efficiently implemented in practice. The research will build on and extend recent advances in the ergodic theory of nonlinear filters. Partially observed stochastic systems are ubiquitous in a wide range of disciplines including signal processing, communications, navigation and tracking, robotics, data assimilation and forecasting, bioinformatics, physics, economics and finance. In such problems, one is faced with two major difficulties: uncertainty in the dynamics of the system of interest, and the limited availability of information. This project aims to understand how one can best make decisions in an uncertain environment when only partial information is available. The development of a mathematical theory characterizing the properties of optimal decisions can help elucidate the fundamental limitations one faces in making decisions with limited information, as well as lead to practical algorithms for making near-optimal decisions which can be used in applications.