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).

This paper examines whether temporal difference methods for training connectionist networks, such as Suttons's TO('\) algorithm, can be successfully appliedto complex real-world problems. A number of important practical issues are identified and discussed from a general theoretical perspective. Thesepractical issues are then examined in the context of a case study in which TO('\) is applied to learning the game of backgammon from the outcome of self-play. This is apparently the first application of this algorithm to a complex nontrivial task. It is found that, with zero knowledge built in, the network is able to learn from scratch to play the entire game at a fairly strong intermediate level of performance, which is clearly better than conventional commercial programs, and which in fact surpasses comparable networks trained on a massive human expert data set. The hidden units in these network have apparently discovered useful features, a longstanding goal of computer games research.

A method for transforming performance evaluation signals distal both in space and time into proximal signals usable by supervised learning algorithms, presentedin [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) controlmay 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. 563 564 Brody ordinatesreached at the end of some motion, for instance. In such cases, supervised learning methods are not directly applicable, and other techniques must be used. Here we study one such technique (proposed for cases where the evaluation is distal in both space and time by [Jordan & Jacobs 90)), analyse a source of its problems, and propose a simple solution for them which leads to fast, efficient learning. We first describe two methods, and then combine them into the "predictive forward modeling" technique with which we are concerned.

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

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 transferof 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 andelemental 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 efforton 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 andfaces multiple sequences of Markovian decision tasks (MDTs).

This article presents a general class of associative reinforcement learning algorithms for connectionist networks containing stochastic units. These algorithms, called REINFORCE algorithms, are shown to make weight adjustments in a direction that lies along the gradient of expected reinforcement in both immediate-reinforcement tasks and certain limited forms of delayed-reinforcement tasks, and they do this without explicitly computing gradient estimates or even storing information from which such estimates could be computed. Specific examples of such algorithms are presented, some of which bear a close relationship to certain existing algorithms while others are novel but potentially interesting in their own right. Also given are results that show how such algorithms can be naturally integrated with backpropagation. We close with a brief discussion of a number of additional issues surrounding the use of such algorithms, including what is known about their limiting behaviors as well as further considerations that might be used to help develop similar but potentially more powerful reinforcement learning algorithms.

This paper examines whether temporal difference methods for training connectionist networks, such as Sutton's TD(λ) algorithm, can be successfully applied to complex real-world problems. A number of important practical issues are identified and discussed from a general theoretical perspective. These practical issues are then examined in the context of a case study in which TD(λ) is applied to learning the game of backgammon from the outcome of self-play. This is apparently the first application of this algorithm to a complex non-trivial task. It is found that, with zero knowledge built in, the network is able to learn from scratch to play the entire game at a fairly strong intermediate level of performance, which is clearly better than conventional commercial programs, and which in fact surpasses comparable networks trained on a massive human expert data set.

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