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.

This paper presents a new approach to hierarchical reinforcement learning based on decomposing the target Markov decision process (MDP) into a hierarchy of smaller MDPs and decomposing the value function of the target MDP into an additive combination of the value functions of the smaller MDPs. The decomposition, known as the MAXQ decomposition, has both a procedural semantics---as a subroutine hierarchy---and a declarative semantics---as a representation of the value function of a hierarchical policy. MAXQ unifies and extends previous work on hierarchical reinforcement learning by Singh, Kaelbling, and Dayan and Hinton. It is based on the assumption that the programmer can identify useful subgoals and define subtasks that achieve these subgoals. By defining such subgoals, the programmer constrains the set of policies that need to be considered during reinforcement learning. The MAXQ value function decomposition can represent the value function of any policy that is consisten...

A preliminary unedited version of this paper was incorrectly published as part of Volume

In this paper, we present a method for recognising an agent's behaviour in dynamic, noisy, uncertain domains, and across multiple levels of abstraction. We term this problem on-line plan recognition under uncertainty and view it generally as probabilistic inference on the stochastic process representing the execution of the agent's plan. Our contributions in this paper are twofold. In terms of probabilistic inference, we introduce the Abstract Hidden Markov Model (AHMM), a novel type of stochastic processes, provide its dynamic Bayesian network (DBN) structure and analyse the properties of this network. We then describe an application of the Rao-Blackwellised Particle Filter to the AHMM which allows us to construct an ecient, hybrid inference method for this model. In terms of plan recognition, we propose a novel plan recognition framework based on the AHMM as the plan execution model. The Rao-Blackwellised hybrid inference for AHMM can take advantage of the independence properties inherent in a model of plan execution, leading to an algorithm for online probabilistic plan recognition that scales well with the number of levels in the plan hierarchy. This illustrates that while stochastic models for plan execution can be complex, they exhibit special structures which, if exploited, can lead to efficient plan recognition algorithms. We demonstrate the usefulness of the AHMM framework via a behaviour recognition system in a complex spatial environment using distributed video surveillance data.

An open problem in reinforcement learning is discovering hierarchical structure. HEXQ, an algorithm which automatically attempts to decompose and solve a model-free factored MDP hierarchically is described. By searching for aliased Markov sub-space regions based on the state variables the algorithm uses temporal and state abstraction to construct a hierarchy of interlinked smaller MDPs.

We present a new general framework for online probabilistic plan recognition called the Abstract Hidden Markov Memory Model (AHMEM). The new model is an extension of the existing Abstract Hidden Markov Model to allow the policy to have internal memory which can be updated in a Markov fashion. We show that the AHMEM can represent a richer class of probabilistic plans, and at the same time derive an efficient algorithm for plan recognition in the AHMEM based on the RaoBlackwellised Particle Filter approximate inference method.

Decision making usually involves choosing among different courses of action over a broad range of time scales. For instance, a person planning a trip to a distant location makes high-level decisions regarding what means of transportation to use, but also chooses low-level actions, such as the movements for getting into a car. The problem of picking an appropriate time scale for reasoning and learning has been explored in artificial intelligence, control theory and robotics. In this dissertation we develop a framework that allows novel solutions to this problem, in the context of Markov Decision Processes (MDPs) and reinforcement learning. In this dissertation, we present a general framework for prediction, control and learning at multipl...

We present a new method for automatically creating useful temporal abstractions in reinforcement learning. We argue that states that allow the agent to transition to a different region of the state space are useful subgoals, and propose a method for identifying them using the concept of relative novelty. When such a state is identified, a temporallyextended activity (e.g., an option) is generated that takes the agent efficiently to this state. We illustrate the utility of the method in a number of tasks. 1.

This paper presents two new approaches to decomposing and solving large Markov decision problems (MDPs), a partial decoupling method and a complete decoupling method. In these approaches, a large, stochastic decision problem is divided into smaller pieces. The first approach builds a cache of policies for each part of the problem independently, and then combines the pieces in a separate, light-weight step. A second approach also divides the problem into smaller pieces, but information is communicatedbetween the different problem pieces, allowing intelligent decisions to be made about which piece requires the most attention. Both approaches can be used to find optimal policies or approximately optimal policies with provable bounds. These algorithms also provide a framework for the efficient transfer of knowledge across problems that share similar structure. 1 Introduction The Markov Decision Problem (MDP) framework provides a formal framework for modeling a large variety of stochastic,...

Eligibility traces have been shown to speed reinforcement learning, to make it more robust to hidden states, and to provide a link between Monte Carlo and temporal-difference methods. Here we generalize eligibility traces to off-policy learning, in which one learns about a policy different from the policy that generates the data. Off-policy methods can greatly multiply learning, as many policies can be learned about from the same data stream, and have been identified as particularly useful for learning about subgoals and temporally extended macro-actions. In this paper we consider the off-policy version of the policy evaluation problem, for which only one eligibility trace algorithm is known, a Monte Carlo method. We analyze and compare this and four new eligibility trace algorithms, emphasizing their relationships to the classical statistical technique known as importance sampling. Our main results are 1) to establish the consistency and bias properties of the new methods and 2) to empirically rank the new methods, showing improvement over one-step and Monte Carlo methods. Our results are restricted to model-free, table-lookup methods and to offline updating (at the end of each episode) although several of the algorithms could be applied more generally. 1.