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.

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.

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 present a computationally efficient algorithm for function approximation with piecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the method of fitting the residual. The task of fitting individual nodes is accomplished using a new algorithm that searchs for the best fit by solving a sequence of Quadratic Programming problems. This approach offers significant advantages over derivative-based search algorithms (e.g.

We present a computationally efficient algorithm for function approximation with piecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the method of fitting the residual. The task of fitting individual nodes is accomplished using a new algorithm that searchs for the best fit by solving a sequence of Quadratic Programming problems. This approach offers significant advantages over derivative-based search algorithms (e.g.

We present a computationally efficient algorithm for function approximation withpiecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the method of fitting the residual. The task of fitting individual nodes is accomplished usinga new algorithm that searchs for the best fit by solving a sequence of Quadratic Programming problems. This approach offers significantadvantages over derivative-based search algorithms (e.g.

The Second International Symposium on Intelligent Data Analysis (IDA97) was held at Birkbeck College, University of London, on 4 to 6 August 1997. The main theme of IDA97 was to reason about how to analyze data,perhaps as human analysts do, by exploiting many methods from diverse disciplines. This article outlines several key issues and challenges, discusses how they were addressed at the conference, and presents opportunities for further work in the field.

We present new results about the temporal-difference learning algorithm, as applied to approximating the cost-to-go function of a Markov chain using linear function approximators. The algorithm we analyze performs online updating of a parameter vector during a single endless trajectory of an aperiodic irreducible finite state Markov chain. Results include convergence (with probability 1), a characterization of the limit of convergence, and a bound on the resulting approximation error. In addition to establishing new and stronger results than those previously available, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporal-difference learning. Furthermore, we discuss the implications of two counterexamples with regards to the Significance of online updating and linearly parameterized function approximators. 1 INTRODUCTION The problem of predicting the expected long-term future cost (or reward) of a stochastic dynamic system manifests itself in both time-series prediction and control.

The Support Vector (SV) method was recently proposed for estimating regressions, constructing multidimensional splines, and solving linear operator equations [Vapnik, 1995]. In this presentation we report results of applying the SV method to these problems.

We present new results about the temporal-difference learning algorithm, as applied to approximating the cost-to-go function of a Markov chain using linear function approximators. The algorithm we analyze performs online updating of a parameter vector during a single endless trajectory of an aperiodic irreducible finite state Markov chain. Results include convergence (with probability 1), a characterization of the limit of convergence, and a bound on the resulting approximation error. In addition to establishing new and stronger results than those previously available, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporal-difference learning. Furthermore, we discuss the implications of two counterexamples with regards to the Significance of online updating and linearly parameterized function approximators. 1 INTRODUCTION The problem of predicting the expected long-term future cost (or reward) of a stochastic dynamic system manifests itself in both time-series prediction and control.