In this paper, we bring techniques from operations research to bear on the problem of choosing optimal actions in partially observable stochastic domains. We begin by introducing the theory of Markov decision processes (mdps) and partially observable mdps (pomdps). We then outline a novel algorithm for solving pomdps offline and show how, in some cases, a finite-memory controller can be extracted from the solution to a pomdp. We conclude with a discussion of how our approach relates to previous work, the complexity of finding exact solutions to pomdps, and of some possibilities for finding approximate solutions.

Discrete Bayesian models have been used to model uncertainty for mobile-robot navigation, but the question of how actions should be chosen remains largely unexplored. This paper presents the optimal solution to the problem, formulated as a partially observable Markov decision process. Since solving for the optimal control policy is intractable, in general, it goes on to explore a variety of heuristic control strategies. The control strategies are compared experimentally, both in simulation and in runs on a robot. 1 Introduction A robot that delivers items and performs errands in an office environment needs to be able to navigate robustly. It should be able to overcome errors in perception and action, at worst getting lost for some period of time, but then being able to recover by re-localizing itself and continuing with its task. The Bayesian framework is particularly appropriate for modeling the robot's belief about its location (or, more generally, the state of the world). It suppl...

Sequential decision making is a fundamental task faced by any intelligent agent in an extended interaction with its environment; it is the act of answering the question "What should I do now?" In this thesis, I show how to answer this question when "now" is one of a finite set of states, "do" is one of a finite set of actions, "should" is maximize a long-run measure of reward, and "I" is an automated planning or learning system (agent). In particular,

Most exact algorithms for general partially observable Markov decision processes (pomdps) use a form of dynamic programming in which a piecewise-linear and convex representation of one value function is transformed into another. We examine variations of the "incremental pruning" method for solving this problem and compare them to earlier algorithms from theoretical and empirical perspectives. We find that incremental pruning is presently the most efficient exact method for solving pomdps. 1 INTRODUCTION Partially observable Markov decision processes (pomdps) model decision theoretic planning problems in which an agent must make a sequence of decisions to maximize its utility given uncertainty in the effects of its actions and its current state (Cassandra, Kaelbling, & Littman 1994; White 1991). At any moment in time, the agent is in one of a finite set of possible states S and must choose one of a finite set of possible actions A. After taking action a 2 A from state s 2 S, the agent...

Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a consequence of computing an exact, optimal policy over the entire belief space. However, in real-world POMDP problems, computing the optimal policy for the full belief space is often unnecessary for good control even for problems with complicated policy classes. The beliefs experienced by the controller often lie near a structured, low-dimensional manifold embedded in the high-dimensional belief space. Finding a good approximation to the optimal value function for only this manifold can be much easier than computing the full value function. We introduce a new method for solving large-scale POMDPs by reducing the dimensionality of the belief space. We use Exponential family Principal Components Analysis (Collins, Dasgupta, & Schapire, 2002) to represent sparse, high-dimensional belief spaces using low-dimensional sets of learned features of the belief state. We then plan only in terms of the low-dimensional belief features. By planning in this low-dimensional space, we can find policies for POMDP models that are orders of magnitude larger than models that can be handled by conventional techniques. We demonstrate the use of this algorithm on a synthetic problem and on mobile robot navigation tasks. 1.

This paper studies the problem of dynamic scheduling of multi-mode sensor resources for the problem of classification of multiple unknown objects. Because of the uncertain nature of the object types, the problem is formulated as a partially observed Markov decision problem with a large state space. The paper describes a hierarchical algorithm approach for e#cient solution of sensor scheduling problems with large numbers of objects, based on combination of stochastic dynamic programming and nondi#erentiable optimization techniques. The algorithm is illustrated with an application involving classification of 10,000 unknown objects. 1 Introduction Many modern avionics systems include multiple sensors as well as individual sensors capable of focusing on different objects with di#erent modes. In order to achieve an accurate possible representation of all objects of interest, it is important to coordinate the allocation and scheduling of the di#erent sensors and sensor modes across the di#...

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Statistical methods have long been the dominant approach in speech recognition and probabilistic modelling in ASR is now a mature technology. The use of statistical methods in other areas of spoken dialogue is however more recent and rather less mature. This paper reviews spoken dialogue systems from a statistical modelling perspective. The complete system is first presented as a partially observable Markov decision process. The various sub-components are then exposed by introducing appropriate intermediate variables. Samples of existing work are reviewed within this framework, including dialogue control and optimisation, semantic interpretation, goal detection, natural language generation and synthesis.

We show that for several variations of partially observable Markov decision processes, polynomial-time algorithms for nding control policies are unlikely to or simply don't have guarantees of nding policies within a constant factor or a constant summand of optimal. Here "unlikely" means \unless some complexity classes collapse," where the collapses considered are P = NP, P = PSPACE, or P = EXP. Until or unless these collapses are shown to hold, any control-policy designer must choose between such performance guarantees and ecient computation.

We examine the problem of performing exact dynamic-programming updates in partially observable Markov decision processes (pomdps) from a computational complexity viewpoint. Dynamic-programming updates are a crucial operation in a wide range of pomdp solution methods and we find that it is intractable to perform these updates on piecewise-linear convex value functions for general pomdps. We offer a new algorithm, called the witness algorithm, which can compute updated value functions efficiently on a restricted class of pomdps in which the number of linear facets is not too great. We compare the witness algorithm to existing algorithms analytically and empirically and find that it is the fastest algorithm over a wide range of pomdp sizes.