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.

Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives adopted in these areas often differ in substantial ways, many planning problems of interest to researchers in these fields can be modeled as Markov decision processes (MDPs) and analyzed using the techniques of decision theory. This paper presents an overview and synthesis of MDP-related methods, showing how they provide a unifying framework for modeling many classes of planning problems studied in AI. It also describes structural properties of MDPs that, when exhibited by particular classes of problems, can be exploited in the construction of optimal or approximately optimal policies or plans. Planning problems commonly possess structure in the reward and value functions used to de...

Learning, planning, and representing knowledge at multiple levels of temporal abstraction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforcement learning and Markov decision processes (MDPs). We extend the usual notion of action in this framework to include options---closed-loop policies for taking action over a period of time. Examples of options include picking up an object, going to lunch, and traveling to a distant city, as well as primitive actions such as muscle twitches and joint torques. Overall, we show that options enable temporally abstract knowledge and action to be included in the reinforcement learning framework in a natural and general way. In particular, we show that options may be used interchangeably with primitive actions in planning methods such as dynamic programming and in learning methods such as Q-learning.

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,

Classic heuristic search algorithms can find solutions that take the form of a simple path (A*), a tree, or an acyclic graph (AO*). In this paper, we describe a novel generalization of heuristic search, called LAO*, that can find solutions with loops. We show that LAO* can be used to solve Markov decision problems and that it shares the advantage heuristic search has over dynamic programming for other classes of problems. Given a start state, it can find an optimal solution without evaluating the entire state space. 2001 Elsevier Science B.V. All rights reserved. Keywords: Heuristic search; Dynamic programming; Markov decision problems 1.

Markov decision problems (MDPs) provide the foundations for a number of problems of interest to AI researchers studying automated planning and reinforcement learning. In this paper, we summarize results regarding the complexity of solving MDPs and the running time of MDP solution algorithms. We argue that, although MDPs can be solved efficiently in theory, more study is needed to reveal practical algorithms for solving large problems quickly. To encourage future research, we sketch some alternative methods of analysis that rely on the structure of MDPs.

actions, or macro-actions, in the solution of Markov decision processes. Unlike current models that combine both primitive actions and macro-actions and leave the state space unchanged, we propose a hierarchical model (using an abstract MDP) that works with macro-actions only, and that significantly reduces the size of the state space. This is achieved by treating macroactions as local policies that act in certain regions MDP to those at the boundaries of regions. The abstract MDP approximates the original and can be solved more efficiently. We discuss several ways in which macro-actions can be generated to ensure good solution quality. Finally, we consider ways in which macro-actions can be reused to solve multiple, related MDPs; and we show that this can justify the computational overhead of macro-action generation. 1

This dissertation investigates the use of hierarchy and problem decomposition as a means of solving large, stochastic, sequential decision problems. These problems are framed as Markov decision problems (MDPs). The new technical content of this dissertation begins with a discussion of the concept of temporal abstraction. Temporal abstraction is shown to be equivalent to the transformation of a policy defined over a region of an MDP to an action in a semi-Markov decision problem (SMDP). Several algorithms are presented for performing this transformation efficiently. This dissertation introduces the HAM method for generating hierarchical, temporally abstract actions. This method permits the partial specification of abstract actions in a way that corresponds to an abstract plan or strategy. Abstr...

We use the notion of stochastic bisimulation homogeneity to analyze planning problems represented as Markov decision processes (MDPs). Informally, a partition of the state space for an MDP is said to be homogeneous if for each action, states in the same block have the same probability of being carried to each other block. We provide an algorithm for finding the coarsest homogeneous refinement of any partition of the state space of an MDP. The resulting partition can be used to construct a reduced MDP which is minimal in a well defined sense and can be used to solve the original MDP. Our algorithm is an adaptation of known automata minimization algorithms, and is designed to operate naturally on factored or implicit representations in which the full state space is never explicitly enumerated. We show that simple variations on this algorithm are equivalent or closely similar to several different recently published algorithms for finding optimal solutions to (partially ...

Most real world environments are non-deterministic. Automatic plan formation in non-deterministic domains is, however, still an open problem. In this paper we present a practical algorithm for the automatic generation of solutions to planning problems in nondeterministic domains. Our approach has the following main features. First, the planner generates Universal Plans, and exploits the compactness of OBDD's (Ordered Binary Decision Diagrams) to express in a practical way plans of extremely large size. Second, the planner generates plans which are guaranteed to achieve the goal in spite of non-determinism, if such plans exist. Otherwise, the planner generates plans which encode iterative trial-and-error strategies (e.g. try to pick up a block until succeed), which are guaranteed to achieve the goal under the assumption that if there is a non-deterministic possibility for the iteration to terminate, this will not be ignored forever. Third, the implementation of the pla...