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...

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...

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...

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,...

. Reinforcement learning addresses the problem of learning optimal policies for sequential decision-making problems involving stochastic operators and numerical reward functions rather than the more traditional deterministic operators and logical goal predicates. In many ways, reinforcement learning research is recapitulating the development of classical research in planning and problem solving. After studying the problem of solving "flat" problem spaces, researchers have recently turned their attention to hierarchical methods that incorporate subroutines and state abstractions. This paper gives an overview of the MAXQ value function decomposition and its support for state abstraction and action abstraction. 1 Introduction Reinforcement learning studies the problem of a learning agent that interacts with an unknown, stochastic, but fully-observable environment. This problem can be formalized as a Markov decision process (MDP), and reinforcement learning research has develop...

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In robotics and other control applications it is commonplace to have a preexisting set of controllers for solving subtasks, perhaps hand-crafted or previously learned or planned, and still face a difficult problem of how to choose and switch among the controllers to solve an overall task as well as possible. In this paper we present a framework based on Markov decision processes and semi-Markov decision processes for phrasing this problem, a basic theorem regarding the improvement in performance that can be obtained by switching flexibly between given controllers, and example applications of the theorem. In particular, we show how an agent can plan with these high-level controllers and then use the results of such planning to find an even better plan, by ...

Several researchers have proposed reinforcement learning methods that obtain ad-vantages in learning by using temporally extended actions, or macro-actions, but none has carefully analyzed what these advantages are. In this paper, we separate and analyze two advantages of using macro-actions in reinforcement learning: the effect on exploratory behavior, independent of learning, and the effect on the speed with which the learning process propagates accurate value information. We empirically measure the separate contributions of these two effects in gridworld and simulated robotic environments. In these environments, both effects were signi cant, but the effect of value propagation was larger. We also compare the accelerations of value propagation due to macro-actions and eligibility traces in the gridworld environment. Although eligibility traces increased the rate of convergence to the optimal value function compared to learning with macro-actions but without eligibility traces, eligibility traces did not permit the optimal policy to be learned as quickly as it was using macro-actions.

We consider the reuse of policies for previous MDPs in learning on a new MDP, under the assumption that the vector of parameters of each MDP is drawn from a fixed probability distribution. We use the options framework, in which an option consists of a set of initiation states, a policy, and a termination condition. We use an option called a reuse option, for which the set of initiation states is the set of all states, the policy is a combination of policies from the old MDPs, and the termination condition is based on the number of time steps since the option was initiated. Given policies for m of the MDPs from the distribution, we construct reuse options from the policies and compare performance on an m + 1st MDP both with and without various reuse options. We find that reuse options can speed initial learning of the m+ 1st task. We also present a distribution of MDPs for which reuse options can slow initial learning. We discuss reasons for this and suggest other ways to design reuse options.

One of the original motivations for the use of temporally extended actions, or options, in reinforcement learning was to enable the transfer of learned value functions or policies to new problems. Many experimenters have used options to speed learning on single problems, but options have not been studied in depth as a tool for transfer. In this paper we introduce a formal model of a learning problem as a distribution of Markov Decision Problems (MDPs). Each MDP represents a task the agent will have to solve. Our model can also be viewed as a partially observable Markov decision problem (POMDP), with a special structure that we describe. We study two learning algorithms, one which keeps a single value function that generalizes across tasks, and an incremental POMDPinspired method maintaining separate value functions for each task. We evaluate the learning algorithms on an extension of the Mountain Car domain, in terms of both learning speed and asymptotic performance. Empi...