Finite Approximations in Discrete-Time Stochastic Control

Description

In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original models and the methods are general enough that researchers can build corresponding approximation results, typically with no additional assumptions. Front Matter ....Pages i-vii Introduction and Summary (Naci Saldi, Tamás Linder, Serdar Yüksel)....Pages 1-11 Front Matter ....Pages 13-13 Prelude to Part I (Naci Saldi, Tamás Linder, Serdar Yüksel)....Pages 15-21 Finite-Action Approximation of Markov Decision Processes (Naci Saldi, Tamás Linder, Serdar Yüksel)....Pages 23-48 Finite-State Approximation of Markov Decision Processes (Naci Saldi, Tamás Linder, Serdar Yüksel)....Pages 49-97 Approximations for Partially Observed Markov Decision Processes (Naci Saldi, Tamás Linder, Serdar Yüksel)....Pages 99-123 Approximations for Constrained Markov Decision Problems (Naci Saldi, Tamás Linder, Serdar Yüksel)....Pages 125-149 Front Matter ....Pages 151-151 Prelude to Part II (Naci Saldi, Tamás Linder, Serdar Yüksel)....Pages 153-157 Finite Model Approximations in Decentralized Stochastic Control (Naci Saldi, Tamás Linder, Serdar Yüksel)....Pages 159-175 Asymptotic Optimality of Finite Models for Witsenhausen’s Counterexample and Beyond (Naci Saldi, Tamás Linder, Serdar Yüksel)....Pages 177-188 Back Matter ....Pages 189-198