Partially Observed Markov Decision Processes: Filtering, Learning and Controlled Sensing

by Vikram Krishnamurthy

Overview

Covering formulation, algorithms and structural results and linking theory to real-world applications in controlled sensing (including social learning, adaptive radars and sequential detection), this book focuses on the conceptual foundations of partially observed Markov decision processes (POMDPs). It emphasizes structural results in stochastic dynamic programming, enabling graduate students and researchers in engineering, operations research, and economics to understand the underlying unifying themes without getting weighed down by mathematical technicalities. In light of major advances in machine learning over the past decade, this edition includes a new Part V on inverse reinforcement learning as well as a new chapter on non-parametric Bayesian inference (for Dirichlet processes and Gaussian processes), variational Bayes and conformal prediction.

Product Details

ISBN-13:	9781009449434
Publisher:	Cambridge University Press
Publication date:	06/05/2025
Edition description:	2nd ed.
Pages:	651
Product dimensions:	7.28(w) x 10.20(h) x 1.57(d)

About the Author

Vikram Krishnamurthy is Professor of Electrical and Computer Engineering at Cornell University. From 2002 to 2016, he was Professor and Senior Canada Research Chair in Statistical Signal Processing at the University of British Columbia. His research contributions are in statistical signal processing, stochastic optimization and control, with applications in social networks, adaptive radar systems and biological ion channels. He is a Fellow of IEEE and served as Distinguished Lecturer for the IEEE Signal Processing Society and Editor-in-Chief of IEEE Journal of Selected Topics in Signal Processing. He was awarded an honorary doctorate from the Royal Institute of Technology (KTH) Sweden in 2014.

Table of Contents

Preface to revised edition; Notation; 1. Introduction; I. Stochastic Models and Bayesian Filtering: 2. Stochastic state space model; 3. Optimal filtering; 4. Algorithms for maximum likelihood parameter estimation; 5. Multi-agent sensing: social learning and data incest; 6. Nonparametric Bayesian inference; II. POMDPs: Models and Applications: 7. Fully observed Markov decision processes; 8. Partially observed Markov decision processes; 9. POMDPs in controlled sensing and sensor scheduling; III. POMDP Structural Results: 10. Structural results for Markov decision processes; 11. Structural results for optimal filters; 12. Monotonicity of value function for POMDPs; 13. Structural results for stopping-time POMDPs; 14. Stopping-Time POMDPs for quickest detection; 15. Myopic policy bounds for POMDPs and sensitivity to model parameters; IV. Stochastic Gradient Algorithms and Reinforcement Learning: 16. Stochastic optimization and gradient estimation; 17. Reinforcement learning; 18. Stochastic gradient algorithms: convergence analysis; 19. Discrete stochastic optimization; V. Inverse Reinforcement Learning: 20. Revealed preferences for inverse reinforcement learning; 21. Bayesian inverse reinforcement learning; Appendix A. Short primer on stochastic stimulation; Appendix B. Continuous-time HMM filters; Appendix C. Discrete-time Martingales; Appendix D. Markov processes; Appendix E. Some limit theorems in statistics; Appendix F. Summary of POMDP algorithms; Bibliography; Index.

Editorial Reviews

‘This book uniquely offers a comprehensive treatment of structural results for Partially Observable Markov Decision Processes (POMDPs), utilizing submodularity and stochastic orders. The new edition expands its scope by introducing essential results in nonparametric Bayes, stochastic optimization, and inverse reinforcement learning, making it an invaluable resource as both a textbook and reference.’ Bo Wahlberg, KTH Royal Institute of Technology, Sweden

‘This book is a tour-de-force on POMDPs and controlled sensing, featuring insightful treatment of foundational concepts in optimal filtering, stochastic control, and stochastic optimization. The new edition introduces innovative methods for detecting cognitive sensors through inverse reinforcement learning from a microeconomic perspective-critical for radar systems, signal processing, and control researchers.’ Muralidhar Rangaswamy, Air Force Research Laboratory, U.S.

‘An outstanding advanced graduate-level introduction to the increasingly important topic of partially observed Markov decision processes. The book is a delight to read - comprehensive, clear, up-to-date and insightful while preserving rigor. An essential resource for both researchers seeking to further advance the field and practitioners wishing to implement stochastic control in real engineering systems.’ Rob Evans, University of Melbourne

From the Publisher