One way to speed up reinforcement learning is to enable learning to happen simultaneously at multiple resolutions in space and time. This paper shows how to create a Q-Iearning managerial hierarchy how to set tasks to their submanagersin which high level managers learn how to satisfy them. Sub-managerswho, in turn, learn understand their managers' commands. Theyneed not initially simply learn to maximise their reinforcement in the context of the current command. We illustrate the system using a simple maze task .. As the system learns how to get around, satisfying commands at the multiple than standard, flat, Q-Iearninglevels, it explores more efficiently and builds a more comprehensive map. 1 INTRODUCTION Straightforward reinforcement learning has been quite successful at some relatively thecomplex tasks like playing backgammon (Tesauro, 1992).

We present a local learning rule in which Hebbian learning is conditional on an incorrect prediction of a reinforcement signal. We propose a biological interpretation of such a framework and display its utility through examples in which the reinforcement signal is cast as the delivery of a neuromodulator to its target. Three exam pIes are presented which illustrate how this framework can be applied to the development of the oculomotor system. 1 INTRODUCTION Activity-dependent accounts of the self-organization of the vertebrate brain have relied ubiquitously on correlational (mainly Hebbian) rules to drive synaptic learning. Inthe brain, a major problem for any such unsupervised rule is that many different kinds of correlations exist at approximately the same time scales and each is effectively noise to the next. For example, relationships within and between the retinae among variables such as color, motion, and topography may mask one another and disrupt their appropriate segregation at the level of the thalamus or cortex.

Machine Learning, 13, 103–130.

Tech. rep. NU-CCS-93-14, College of Computer Science, Northeastern University.

TO('\) is an algorithm for adjusting the weights in a connectionist network which 259 260 Tesauro has the following form:

A method for transforming performance evaluation signals distal both in space and time into proximal signals usable by supervised learning algorithms, presented in [Jordan & Jacobs 90], is examined. A simple observation concerning differentiation through models trained with redundant inputs (as one of their networks is) explains a weakness in the original architecture and suggests a modification: an internal world model that encodes action-space exploration and, crucially, cancels input redundancy to the forward model is added. Learning time on an example task, cartpole balancing, is thereby reduced about 50 to 100 times. 1 INTRODUCTION In many learning control problems, the evaluation used to modify (and thus improve) control may not be available in terms of the controller's output: instead, it may be in terms of a spatial transformation of the controller's output variables (in which case we shall term it as being "distal in space"), or it may be available only several time steps into the future (termed as being "distal in time"). For example, control of a robot arm may be exerted in terms of joint angles, while evaluation may be in terms of the endpoint cartesian coordinates; furthermore, we may only wish to evaluate the endpoint coordinates reached after a certain period of time: the co- ·Current address: Computation and Neural Systems Program, California Institute of Technology, Pasadena CA.

Following Simon's (1969) observation that complex behaviour may simply be the reflection of a complex environment a number of researchers (eg.

TO('\) is an algorithm for adjusting the weights in a connectionist network which 259 260 Tesauro has the following form:

I present a modular network architecture and a learning algorithm based on incremental dynamic programming that allows a single learning agent to learn to solve multiple Markovian decision tasks (MDTs) with significant transfer of learning across the tasks. I consider a class of MDTs, called composite tasks, formed by temporally concatenating a number of simpler, elemental MDTs. The architecture is trained on a set of composite and elemental MDTs. The temporal structure of a composite task is assumed to be unknown and the architecture learns to produce a temporal decomposition. It is shown that under certain conditions the solution of a composite MDT can be constructed by computationally inexpensive modifications of the solutions of its constituent elemental MDTs. 1 INTRODUCTION Most applications of domain independent learning algorithms have focussed on learning single tasks. Building more sophisticated learning agents that operate in complex environments will require handling multiple tasks/goals (Singh, 1992). Research effort on the scaling problem has concentrated on discovering faster learning algorithms, and while that will certainly help, techniques that allow transfer of learning across tasks will be indispensable for building autonomous learning agents that have to learn to solve multiple tasks. In this paper I consider a learning agent that interacts with an external, finite-state, discrete-time, stochastic dynamical environment and faces multiple sequences of Markovian decision tasks (MDTs).

Following Simon's (1969) observation that complex behaviour may simply be the reflection of a complex environment a number of researchers (eg.