A convex analytic approach to Markov decision processes |
| |
Authors: | Vivek S Borkar |
| |
Institution: | (1) Systems Research Center, University of Maryland, 20742 College Park, MD, USA;(2) Present address: Bangalore Center, Tata Institute of Fundamental Research, I.I.Sc. Campus, P.O. Box 1234, 560012 Bangalore, India |
| |
Abstract: | Summary This paper develops a new framework for the study of Markov decision processes in which the control problem is viewed as an optimization problem on the set of canonically induced measures on the trajectory space of the joint state and control process. This set is shown to be compact convex. One then associates with each of the usual cost criteria (infinite horizon discounted cost, finite horizon, control up to an exit time) a naturally defined occupation measure such that the cost is an integral of some function with respect to this measure. These measures are shown to form a compact convex set whose extreme points are characterized. Classical results about existence of optimal strategies are recovered from this and several applications to multicriteria and constrained optimization problems are briefly indicated.Research supported by NSF Grant CDR-85-00108 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|