Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly represented by its own function approximator, independent of the value function, and is updated according to the gradient of expected reward with respect to the policy parameters. Williams's REINFORCE method and actor-critic methods are examples of this approach. Our main new result is to show that the gradient can be written in a form suitable for estimation from experience aided by an approximate action-value or advantage function. Using this result, we prove for the first time that a version of policy iteration with arbitrary differentiable function approximation is convergent to a locally optimal policy.

We propose and analyze a class of actor-critic algorithms for simulation-based optimization of a Markov decision process over a parameterized family of randomized stationary policies. These are two-time-scale algorithms in which the critic uses TD learning with a linear approximation architecture and the actor is updated in an approximate gradient direction based on information provided by the critic. We show that the features for the critic should span a subspace prescribed by the choice of parameterization of the actor. We conclude by discussing convergence properties and some open problems.

Many researchers have explored methods for hierarchical reinforcement learning (RL) with temporal abstractions, in which abstract actions are defined that can perform many primitive actions before terminating. However, little is known about learning with state abstractions, in which aspects of the state space are ignored. In previous work, we developed the MAXQ method for hierarchical RL. In this paper, we define five conditions under which state abstraction can be combined with the MAXQ value function decomposition. We prove that the MAXQ-Q learning algorithm converges under these conditions and show experimentally that state abstraction is important for the successful application of MAXQ-Q learning.

Recently, a number of authors have proposed treating dialogue systems as Markov decision processes (MDPs). However, the practical application ofMDP algorithms to dialogue systems faces a number of severe technical challenges. We have built a general software tool (RLDS, for Reinforcement Learning for Dialogue Systems) based on the MDP framework, and have applied it to dialogue corpora gathered from two dialogue systems built at AT&T Labs. Our experiments demonstrate that RLDS holds promise as a tool for "browsing" and understanding correlations in complex, temporally dependent dialogue corpora.

Recently,a number of authorshave proposedtreating dialogue systems as Markov decision processes(MDPs). However,the practicalapplicationofMDP algorithms to dialogue systems faces a numberof severe technicalchallenges.We have built a general software tool (RLDS, for ReinforcementLearning for Dialogue Systems) on the MDP framework, and have applied it to dialogue corpora gatheredbased from two dialoguesystemsbuilt at AT&T Labs. Our experimentsdemonstratethat RLDS holds promise as a tool for "browsing" and understandingcorrelationsin complex, temporallydependentdialogue corpora.

Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining apolicy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly represented by its own function approximator, independent ofthe value function, and is updated according to the gradient of expected reward with respect to the policy parameters. Williams's REINFORCE method and actor-critic methods are examples of this approach. Our main new result is to show that the gradient can be written in a form suitable for estimation from experience aided by an approximate action-value or advantage function. Using this result, we prove for the first time that a version of policy iteration with arbitrary differentiable function approximation is convergent to a locally optimal policy.

We propose and analyze a class of actor-critic algorithms for simulation-based optimization of a Markov decision process over a parameterized family of randomized stationary policies. These are two-time-scale algorithms in which the critic uses TD learning with a linear approximation architecture and the actor is updated in an approximate gradient direction based on information provided bythe critic. We show that the features for the critic should span a subspace prescribed by the choice of parameterization of the actor. We conclude by discussing convergence properties and some open problems.

Forexample, in the Options framework [1,2], the programmer defines a set of macro actions ("options") and provides a policy for each. Learning algorithms (such as semi-Markov Q learning) can then treat these temporally abstract actions as if they were primitives and learn a policy for selecting among them. Closely related is the HAM framework, in which the programmer constructs a hierarchy of finitestate controllers[3]. Each controller can include non-deterministic states (where the programmer was not sure what action to perform). The HAMQ learning algorithm can then be applied to learn a policy for making choices in the non-deterministic states.

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 consistent with the given hierarchy. The decomposition also creates opportunities to exploit state abstractions, so that individual MDPs within the hierarchy can ignore large parts of the state space. This is important for the practical application of the method. This paper defines the MAXQ hierarchy, proves formal results on its representational power, and establishes five conditions for the safe use of state abstractions. The paper presents an online model-free learning algorithm, MAXQ-Q, and proves that it converges with probability 1 to a kind of locally-optimal policy known as a recursively optimal policy, even in the presence of the five kinds of state abstraction. The paper evaluates the MAXQ representation and MAXQ-Q through a series of experiments in three domains and shows experimentally that MAXQ-Q (with state abstractions) converges to a recursively optimal policy much faster than flat Q learning. The fact that MAXQ learns a representation of the value function has an important benefit: it makes it possible to compute and execute an improved, non-hierarchical policy via a procedure similar to the policy improvement step of policy iteration. The paper demonstrates the effectiveness of this non-hierarchical execution experimentally. Finally, the paper concludes with a comparison to related work and a discussion of the design tradeoffs in hierarchical reinforcement learning.

This paper describes a novel method by which a spoken dialogue system can learn to choose an optimal dialogue strategy from its experience interacting with human users. The method is based on a combination of reinforcement learning and performance modeling of spoken dialogue systems. The reinforcement learning component applies Q-learning (Watkins, 1989), while the performance modeling component applies the PARADISE evaluation framework (Walker et al., 1997) to learn the performance function (reward) used in reinforcement learning. We illustrate the method with a spoken dialogue system named ELVIS (EmaiL Voice Interactive System), that supports access to email over the phone. We conduct a set of experiments for training an optimal dialogue strategy on a corpus of 219 dialogues in which human users interact with ELVIS over the phone. We then test that strategy on a corpus of 18 dialogues. We show that ELVIS can learn to optimize its strategy selection for agent initiative, for reading messages, and for summarizing email folders.