We describe the reinforcement learning problem, motivate algorithms which seek an approximation to the Q function, and present new convergence results for two such algorithms. 1 INTRODUCTION AND BACKGROUND Imagine an agent acting in some environment. At time t, the environment is in some state Xt chosen from a finite set of states. The agent perceives Xt, and is allowed to choose an action at from some finite set of actions. Meanwhile, the agent experiences a real-valued cost Ct, chosen from a distribution which also depends only on Xt and at and which has finite mean and variance. Such an environment is called a Markov decision process, or MDP.

Elucidation of the relationship between TD learning and dynamic programming (DP) has provided good theoretical insights (Barto et al., 1995). However, conventional TD algorithms were based on discrete-time, discrete-state formulations. In applying these algorithms to control problems, time, space and action had to be appropriately discretized using a priori knowledge or by trial and error. Furthermore, when a TD algorithm is used for neurobiological modeling, discrete-time operation is often very unnatural. There have been several attempts to extend TD-like algorithms to continuous cases. Bradtke et al. (1994) showed convergence results for DPbased algorithms for a discrete-time, continuous-state linear system with a quadratic cost. Bradtke and Duff (1995) derived TD-like algorithms for continuous-time, discrete-state systems (semi-Markov decision problems). Baird (1993) proposed the "advantage updating" algorithm by modifying Q-Iearning so that it works with arbitrary small time steps.

A method for incorporating context-dependent phone classes in a connectionist-HMM hybrid speech recognition system is introduced. A modular approach is adopted, where single-layer networks discriminate between different context classes given the phone class and the acoustic data. The context networks are combined with a context-independent (CI) network to generate context-dependent (CD) phone probability estimates. Experiments show an average reduction in word error rate of 16% and 13% from the CI system on ARPA 5,000 word and SQALE 20,000 word tasks respectively. Due to improved modelling, the decoding speed of the CD system is more than twice as fast as the CI system.

Recent efforts to identify EEG sources have focused mostly on verforming spatial segregation and localization of source activity [4]. By applying the leA algorithm of Bell and Sejnowski [1], we attempt to completely separate the twin problems of source identification (What) and source localization (Where). The leA algorithm derives independent sources from highly correlated EEG signals statistically and without regard to the physical location or configuration of the source generators. Rather than modeling the EEG as a unitary output of a multidimensional dynamical system,or as "the roar of the crowd" of independent microscopic generators, we suppose that the EEG is the output of a number of statistically independent but spatially fixed potential-generating systems which may either be spatially restricted or widely distributed.

A method for incorporating context-dependent phone classes in a connectionist-HMM hybrid speech recognition system is introduced. Amodular approach is adopted, where single-layer networks discriminate between different context classes given the phone class and the acoustic data. The context networks are combined with a context-independent (CI) network to generate context-dependent (CD) phone probability estimates. Experiments show an average reduction in word error rate of 16% and 13% from the CI system on ARPA 5,000 word and SQALE 20,000 word tasks respectively. Due to improved modelling, the decoding speed of the CD system is more than twice as fast as the CI system.

In Tesauro's 1992 landmark work on TD--gammon, he showed that the temporal dif--

Elucidation of the relationship between TD learning and dynamic programming (DP) has provided good theoretical insights (Barto et al., 1995). However, conventional TD algorithms were based on discrete-time, discrete-state formulations. In applying these algorithms to control problems, time, space and action had to be appropriately discretized using a priori knowledge or by trial and error. Furthermore, when a TD algorithm is used for neurobiological modeling, discrete-time operation is often very unnatural. There have been several attempts to extend TD-like algorithms to continuous cases. Bradtke et al. (1994) showed convergence results for DPbased algorithms for a discrete-time, continuous-state linear system with a quadratic cost. Bradtke and Duff (1995) derived TD-like algorithms for continuous-time, discrete-state systems (semi-Markov decision problems). Baird (1993) proposed the "advantage updating" algorithm by modifying Q-Iearning so that it works with arbitrary small time steps.

We describe the reinforcement learning problem, motivate algorithms whichseek an approximation to the Q function, and present new convergence results for two such algorithms. 1 INTRODUCTION AND BACKGROUND Imagine an agent acting in some environment. At time t, the environment is in some state Xt chosen from a finite set of states. The agent perceives Xt, and is allowed to choose an action at from some finite set of actions. Meanwhile, the agent experiences a real-valued cost Ct, chosen from a distribution which also depends only on Xt and at and which has finite mean and variance. Such an environment is called a Markov decision process, or MDP.

Reinforcement learning has become one of the most actively studied learning frameworks in the area of intelligent autonomous agents. This article describes the results of a three-day meeting of leading researchers in this area that was sponsored by the National Science Foundation. Because reinforcement learning is an interdisciplinary topic, the workshop brought together researchers from a variety of fields, including machine learning, neural networks, AI, robotics, and operations research. The goals of the meeting were to (1) understand limitations of current reinforcement-learning systems and define promising directions for further research; (2) clarify the relationships between reinforcement learning and existing work in engineering fields, such as operations research; and (3) identify potential industrial applications of reinforcement learning.

As part of a collaboration with the White House Office of Media Affairs, members of the Artificial Intelligence Laboratory at the Massachusetts Institute of Technology designed a system, called COMLINK, that distributes a daily stream of documents released by the Office of Media Affairs. Approximately 4,000 direct subscribers receive information from this service, but more than 100,000 people receive the information through redistribution channels. The information is distributed through e-mail and the World Wide Web. These invalid subscriptions cause a backwash of hundreds of bounced-mail messages each day that must be processed by the operators of the COMLINK system.