Linear Approximations For Factored Markov Decision Processes

A Markov Decision Process (MDP) is a model employed to describe problems in which a decision must be made at each one of several stages, while receiving feedback from the environment. This type of model has been extensively studied in the operations research community and fundamental algorithms have been developed to solve associated problems. However, these algorithms are quite inefficient for very large problems, leading to a need for alternatives; since MDP problems are provably hard on compressed representations, one becomes content even with algorithms which may perform well at least on specific classes of problems. The class of problems we deal with in this thesis allows succinct representations for the MDP as a dynamic Bayes network, and for its solution as a weighted combination of basis functions. We develop novel algorithms for producing, improving, and calculating the error of approximate solutions for MDPs using a compressed representation. Specifically, we develop an efficient branch-and-bound algorithm for computing the Bellman error of the compact approximate solution regardless of its provenance. We introduce an efficient direct linear programming algorithm which, using incremental constraints generation, achieves run times significantly smaller than existing approximate algorithms without much loss of accuracy. We also show a novel direct linear programming algorithm which, instead of employing constraints generation, transforms the exponentially many constraints into a compact form more amenable for tractable solutions. In spite of its perceived importance, the efficient optimization of the Bellman error towards an approximate MDP solution has eluded current algorithms; to this end we propose a novel branch-and-bound approximate policy iteration algorithm which makes direct use of our branch-and-bound method for computing the Bellman error. We further investigate another procedure for obtaining an approximate solution based on the dual of the direct, approximate linear programming formulation for solving MDPs. To address both the loss of accuracy resulting from the direct, approximate linear program solution and the question of where basis functions come from we also develop a principled system able not only to produce the initial set of basis functions, but also able to augment it with new basis functions automatically generated such that the approximation error decreases according to the user's requirements and time limitations.

Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision problems under uncertainty as well as reinforcement learning problems. Written by experts in the field, this book provides a global view of current research using MDPs in artificial intelligence. It starts with an introductory presentation of the fundamental aspects of MDPs (planning in MDPs, reinforcement learning, partially observable MDPs, Markov games and the use of non-classical criteria). It then presents more advanced research trends in the field and gives some concrete examples using illustrative real life applications.

Markov Decision Processes (MDPs) are widely popular in Artificial Intelligence for modeling sequential decision-making scenarios with probabilistic dynamics. They are the framework of choice when designing an intelligent agent that needs to act for long periods of time in an environment where its actions could have uncertain outcomes. MDPs are actively researched in two related subareas of AI, probabilistic planning and reinforcement learning. Probabilistic planning assumes known models for the agent's goals and domain dynamics, and focuses on determining how the agent should behave to achieve its objectives. On the other hand, reinforcement learning additionally learns these models based on the feedback the agent gets from the environment. This book provides a concise introduction to the use of MDPs for solving probabilistic planning problems, with an emphasis on the algorithmic perspective. It covers the whole spectrum of the field, from the basics to state-of-the-art optimal and approximation algorithms. We first describe the theoretical foundations of MDPs and the fundamental solution techniques for them. We then discuss modern optimal algorithms based on heuristic search and the use of structured representations. A major focus of the book is on the numerous approximation schemes for MDPs that have been developed in the AI literature. These include determinization-based approaches, sampling techniques, heuristic functions, dimensionality reduction, and hierarchical representations. Finally, we briefly introduce several extensions of the standard MDP classes that model and solve even more complex planning problems. Table of Contents: Introduction / MDPs / Fundamental Algorithms / Heuristic Search Algorithms / Symbolic Algorithms / Approximation Algorithms / Advanced Notes

This volume contains the proceedings of the 6th Symposium on Abstraction, Reformulation and Approximation (SARA 2005). The symposium was held at Airth Castle, Scotland, UK, from July 26th to 29th, 2005, just prior to the IJCAI 2005 conference in Edinburgh.

A complete resource to Approximate Dynamic Programming (ADP), including on-line simulation code Provides a tutorial that readers can use to start implementing the learning algorithms provided in the book Includes ideas, directions, and recent results on current research issues and addresses applications where ADP has been successfully implemented The contributors are leading researchers in the field

This book provides a unified approach for the study of constrained Markov decision processes with a finite state space and unbounded costs. Unlike the single controller case considered in many other books, the author considers a single controller with several objectives, such as minimizing delays and loss, probabilities, and maximization of throughputs. It is desirable to design a controller that minimizes one cost objective, subject to inequality constraints on other cost objectives. This framework describes dynamic decision problems arising frequently in many engineering fields. A thorough overview of these applications is presented in the introduction. The book is then divided into three sections that build upon each other. The first part explains the theory for the finite state space. The author characterizes the set of achievable expected occupation measures as well as performance vectors, and identifies simple classes of policies among which optimal policies exist. This allows the reduction of the original dynamic into a linear program. A Lagranian approach is then used to derive the dual linear program using dynamic programming techniques. In the second part, these results are extended to the infinite state space and action spaces. The author provides two frameworks: the case where costs are bounded below and the contracting framework. The third part builds upon the results of the first two parts and examines asymptotical results of the convergence of both the value and the policies in the time horizon and in the discount factor. Finally, several state truncation algorithms that enable the approximation of the solution of the original control problem via finite linear programs are given.

Provides a comprehensive survey of techniques to automatically construct basis functions or features for value function approximation in Markov decision processes and reinforcement learning.

The annual AAAI National Conference provides a forum for information exchange and interaction among researchers from all disciplines of AI. Contributions include theoretical, experimental and empirical results. Topics cover principles of cognition, perception and action; the design, application and evaluation of AI algorithms and systems; architectures and frameworks for classses of AI systems; and analyses of tasks and domains in which intelligent systems perform. The Innovative Applications Conference highlights successful application of AI technology and explores issues, methods and lessons learned in the development and deployment of AI applications.