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In this report we show how the class of adaptive prediction methods that Sutton called "temporal difference," or TD, methods are related to the theory of squential decision making. TD methods have been used as "adaptive critics" in connectionist learning systems, and have been proposed as models of animal learning in classical conditioning experiments. Here we relate TD methods to decision tasks formulated in terms of a stochastic dynamical system whose behavior unfolds over time under the influence of a decision maker's actions. Strategies are sought for selecting actions so as to maximize a measure of long-term payoff gain. Mathematically, tasks such as this can be formulated as Markovian decision problems, and numerous methods have been proposed for learning how to solve such problems. We show how a TD method can be understood as a novel synthesis of concepts from the theory of stochastic dynamic programming, which comprises the standard method for solving such tasks when a model of the dynamical system is available, and the theory of parameter estimation, which provides the appropriate context for studying learning rules in the form of equations for updating associative strengths in behavioral models, or connection weights in connectionist networks. Because this report is oriented primarily toward the non-engineer interested in animal learning, it presents tutorials on stochastic sequential decision tasks, stochastic dynamic programming, and parameter estimation.

Abstract. We introduce two new temporal difference (TD) algorithms based on the theory of linear leastsquares function approximation. We define an algorithm we call Least-Squares TD (LS TD) for which we prove probability-one convergence when it is used with a function approximator linear in the adjustable parameters. We then define a recursive version of this algorithm, Recursive Least-Squares TD (RLS TD). Although these new TD algorithms require more computation per time-step than do Sutton's TD(A) algorithms, they are more efficient in a statistical sense because they extract more information from training experiences. We describe a simulation experiment showing the substantial improvement in learning rate achieved by RLS TD in an example Markov prediction problem. To quantify this improvement, we introduce the TD error variance of a Markov chain, arc,, and experimentally conclude that the convergence rate of a TD algorithm depends linearly on ~ro. In addition to converging more rapidly, LS TD and RLS TD do not have control parameters, such as a learning rate parameter, thus eliminating the possibility of achieving poor performance by an unlucky choice of parameters.

Abstract | We survey learning algorithms for recurrent neural networks with hidden units, and put the various techniques into a common framework. We discuss xedpoint learning algorithms, namely recurrent backpropagation and deterministic Boltzmann Machines, and non- xedpoint algorithms, namely backpropagation through time, Elman's history cuto, and Jordan's output feedback architecture. Forward propagation, an online technique that uses adjoint equations, and variations thereof, are also discussed. In many cases, the uni ed presentation leads to generalizations of various sorts. We discuss advantages and disadvantages of temporally continuous neural networks in contrast to clocked ones, continue with some \tricks of the trade" for training, using, and simulating continuous time and recurrent neural networks. We present somesimulations, and at the end, address issues of computational complexity and learning speed.

Introduction 1.1 Learning in Recurrent Networks Connectionist networks having feedback connections are interesting for a number of reasons. Biological neural networks are highly recurrently connected, and many authors have studied recurrent network models of various types of perceptual and memory processes. The general property making such networks interesting and potentially useful is that they manifest highly nonlinear dynamical behavior. One such type of dynamical behavior that has received much attention is that of settling to a fixed stable state, but probably of greater importance both biologically and from an engineering viewpoint are time-varying behaviors. Here we consider algorithms for training recurrent networks to perform temporal supervised learning tasks, in which the specification of desired behavior is in the form of specific examples of input and desired output trajectories. One example of such a task is sequence classification, where

Animation through the numerical simulation of physics-based graphics models offers unsurpassed realism, but it can be computationally demanding. Likewise, finding controllers that enable physics-based models to produce desired animations usually entails formidable computational cost. This paper demonstrates the possibility of replacing the numerical simulation and control of model dynamics with a dramatically more efficient alternative. In particular, we propose the NeuroAnimator, a novel approach to creating physically realistic animation that exploits neural networks. NeuroAnimators are automatically trained off-line to emulate physical dynamics through the observation of physics-based models in action. Depending on the model, its neural network emulator can yield physically realistic animation one or two orders of magnitude faster than conventional numerical simulation. Furthermore, by exploiting the network structure of the NeuroAnimator, we introduce a fast algorithm for learning controllers that enables either physics-based models or their neural network emulators to synthesize motions satisfying prescribed animation goals. We demonstrate NeuroAnimators for passive and active (actuated) rigid body, articulated, and deformable physics-based models.

Continual learning is the constant development of complex behaviors with no final end in mind. It is the process of learning ever more complicated skills by building on those skills already developed. In order for learning at one stage of development to serve as the foundation for later learning, a continual-learning agent should learn hierarchically. CHILD, an agent capable of Continual, Hierarchical, Incremental Learning and Development is proposed, described, tested, and evaluated in this dissertation. CHILD accumulates useful behaviors in reinforcement environments by using the Temporal Transition Hierarchies learning algorithm, also derived in the dissertation. This constructive algorithm generates a hierarchical, higher-order neural network that can be used for predicting context-dependent temporal sequences and can learn sequential-task benchmarks more than two orders of magnitude faster than competing neural-network systems. Consequently, CHILD can quickly solve complicated non...

Reinforcement learning is a type of unsupervised learning for sequential decision making. Qlearning is probably the best-understood reinforcement learning algorithm. In Q-learning, the agent learns a mapping from states and actions to their utilities. An important assumption of Q-learning is the Markovian environment assumption, meaning that any information needed to determine the optimal actions is reflected in the agent's state representation. Consider an agent whose state representation is based solely on its immediate perceptual sensations. When its sensors are not able to make essential distinctions among world states, the Markov assumption is violated, causing a problem called perceptual aliasing. For example, when facing a closed box, an agent based on its current visual sensation cannot act optimally if the optimal action depends on the contents of the box. There are two basic approaches to addressing this problem--- using more sensors or using history to figure out the curren...

A neural network architecture, which models synapses as Finite Impulse Response (FIR) linear filters, is discussed for use in time series prediction. Analysis and methodology are detailed in the context of the Santa Fe Institute Time Series Prediction Competition. Results of the competition show that the FIR network performed remarkably well on a chaotic laser intensity time series. 1 Introduction The goal of time series prediction or forecasting can be stated succinctly as follows: given a sequence y(1); y(2); : : : y(N) up to time N , find the continuation y(N + 1); y(N + 2)::: The series may arise from the sampling of a continuous time system, and be either stochastic or deterministic in origin. The standard prediction approach involves constructing an underlying model which gives rise to the observed sequence. In the oldest and most studied method, which dates back to Yule [1], a linear autoregression (AR) is fit to the data: y(k) = T X n=1 a(n)y(k \Gamma n) + e(k) = y(k) + ...

Previous work on learning regular languages from exemplary training sequences showed that Long Short- Term Memory (LSTM) outperforms traditional recurrent neural networks (RNNs). Here we demonstrate LSTM's superior performance on context free language (CFL) benchmarks for recurrent neural networks (RNNs), and show that it works even better than previous hardwired or highly specialized architectures.