This paper describes some of the interactions of model learning algorithms and planning algorithms we have found in exploring model-based reinforcement learning. The paper focuses on how local trajectoryoptimizers can be used effectively with learned nonparametric models.We find that trajectory planners that are fully consistent with the learned model often have difficulty finding reasonable plansin the early stages of learning. Trajectory planners that balance obeying the learned model with minimizing cost (or maximizing reward) often do better, even if the plan is not fully consistent with the learned model. 1 INTRODUCTION We are exploring the use of nonparametric models in robot learning (Atkeson et al., 1997b; Atkeson and Schaal, 1997). This paper describes the interaction of model learning algorithms and planning algorithms, focusing on how local trajectory optimization canbe used effectively with nonparametric models in reinforcement learning. We find that trajectory optimizers that are fully consistent with the learned model often have difficulty finding reasonable plans in the early stages of learning. The message of this paper is that a planner should not be entirely consistent with the learned model during model-based reinforcement learning.

Peter Dayan E25-210, MIT Cambridge, MA 02139 We provide a model of the standard watermaze task, and of a more challenging task involving novel platform locations, in which rats exhibit one-trial learning after a few days of training. The model uses hippocampal place cells to support reinforcement learning, and also, in an integrated manner, to build and use allocentric coordinates. 1 INTRODUCTION

This article describes a milestone in our research efforts toward the real robot competition in RoboCup. We participated in the middle-size league at RoboCup-97, held in conjunction with the Fifteenth International Joint Conference on Artificial Intelligence in Nagoya, Japan. The most significant features of our team, TRACKIES, are the application of a reinforcement learning method enhanced for real robot applications and the use of an omnidirectional vision system for our goalie that can capture a 360-degree view at any instant in time. The method and the system used are shown with competition results.

In this article, we describe the milestone of our research efforts in our work for the RoboCup middle-size league competition. Reinforcement learning in applying it to real robot applications; we then give our method of coping with these has recently been receiving increased attention issues in the context of RoboCup. Finally, we as a method for robot learning with little or no show our system and the experimental results a priori knowledge and a higher capability for of RoboCup-97. The robot senses the current state First, we follow the explanation of Q-learning of the environment and selects an action. For a more thorough treatment, Based on the state and the action, the environment see Watkins and Dayan (1992).

We have calculated analytical expressions for how the bias and variance of the estimators provided by various temporal difference value estimation algorithms change with offline updates over trials in absorbing Markov chains using lookup table representations. We illustrate classes of learning curve behavior in various chains, and show the manner in which TD is sensitive to the choice of its stepsize and eligibility trace parameters. 1 INTRODUCTION A reassuring theory of asymptotic convergence is available for many reinforcement learning (RL) algorithms. What is not available, however, is a theory that explains the finite-term learning curve behavior of RL algorithms, e.g., what are the different kinds of learning curves, what are their key determinants, and how do different problem parameters effect rate of convergence. Answering these questions is crucial not only for making useful comparisons between algorithms, but also for developing hybrid and new RL methods. In this paper we provide preliminary answers to some of the above questions for the case of absorbing Markov chains, where mean square error between the estimated and true predictions is used as the quantity of interest in learning curves.

By now it is widely accepted that learning a task from scratch, i.e., without any prior knowledge, is a daunting undertaking. Humans, however, rarely attempt to learn from scratch. They extract initial biases as well as strategies how to approach a learning problem from instructions and/or demonstrations of other humans. For learning control, this paper investigates how learning from demonstration can be applied in the context of reinforcement learning. We consider priming the Q-function, the value function, the policy, and the model of the task dynamics as possible areas where demonstrations can speed up learning. In general nonlinear learning problems, only model-based reinforcement learning shows significant speedup after a demonstration, while in the special case of linear quadratic regulator (LQR) problems, all methods profit from the demonstration. In an implementation of pole balancing on a complex anthropomorphic robot arm, we demonstrate that, when facing the complexities of real signal processing, model-based reinforcement learning offers the most robustness for LQR problems. Using the suggested methods, the robot learns pole balancing in just a single trial after a 30 second long demonstration of the human instructor.

A CDP can always be discretized in state space and time and thus reduced to a Markov Decision Problem. Algorithms like Q-Iearning and RTDP as described in [1] can then be applied to produce controls or optimal value functions for a fixed discretization. Problems arise when the discretization needs to be refined, or when multi-grid information needs to be extracted to accelerate the algorithm. The relation of time to state space discretization parameters is crucial in both cases. Therefore 1034 S. Pareigis a mathematical model of the discretized process is introduced, which reflects the properties of the converged empirical process.

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.

Figure 2: The task is to move the cart to the origin as quickly as possible without dropping the pole. The bottom three pictures show a trace of the policy execution obtained after one, two, and three trials (shown in increments of 0.5 seconds) Controller Number of data points used Cost from initial state 17 to build the controller LQR

In cellular telephone systems, an important problem is to dynamically allocate the communication resource (channels) so as to maximize service in a stochastic caller environment. This problem is naturally formulated as a dynamic programming problem and we use a reinforcement learning (RL) method to find dynamic channel allocation policies that are better than previous heuristic solutions. The policies obtained perform well for a broad variety of call traffic patterns.