Designing Computer Games to Facilitate Learning

The aim of this thesis was to explore the design of interactive computer learning environments. The particular learning domain selected was Newtonian dynamics. Newtonian dynamics was chosen because it is an important area of physics with which many students have difficulty and because controlling Newtonian motion takes advantage of the computer's graphics and interactive capabilities. The learning environment involved games which simulated the motion of a spaceship on a display screen. The purpose of the games was to focus the students' attention on various aspects of the implications of Newton's laws.

A Formulation for Active Learning with Applications to Object Detection

We discuss a formulation for active example selection for function learning problems. This formulation is obtained by adapting Fedorov's optimal experiment design to the learning problem. We specifically show how to analytically derive example selection algorithms for certain well defined function classes. We then explore the behavior and sample complexity of such active learning algorithms. Finally, we view object detection as a special case of function learning and show how our formulation reduces to a useful heuristic to choose examples to reduce the generalization error.

Roles of Knowledge in Motor Learning

The goal of this thesis is to apply the computational approach to motor learning, i.e., describe the constraints that enable performance improvement with experience and also the constraints that must be satisfied by a motor learning system, describe what is being computed in order to achieve learning, and why it is being computed. The particular tasks used to assess motor learning are loaded and unloaded free arm movement, and the thesis includes work on rigid body load estimation, arm model estimation, optimal filtering for model parameter estimation, and trajectory learning from practice. Learning algorithms have been developed and implemented in the context of robot arm control. The thesis demonstrates some of the roles of knowledge in learning. Powerful generalizations can be made on the basis of knowledge of system structure, as is demonstrated in the load and arm model estimation algorithms. Improving the performance of parameter estimation algorithms used in learning involves knowledge of the measurement noise characteristics, as is shown in the derivation of optimal filters. Using trajectory errors to correct commands requires knowledge of how command errors are transformed into performance errors, i.e., an accurate model of the dynamics of the controlled system, as is demonstrated in the trajectory learning work. The performance demonstrated by the algorithms developed in this thesis should be compared with algorithms that use less knowledge, such as table based schemes to learn arm dynamics, previous single trajectory learning algorithms, and much of traditional adaptive control.

The Structure of Mathematical Knowledge

This report develops a conceptual framework in which to talk about mathematical knowledge. There are several broad categories of mathematical knowledge: results which contain the traditional logical aspects of mathematics; examples which contain illustrative material; and concepts which include formal and informal ideas, that is, definitions and heuristics.

Explorations of the Practical Issues of Learning Prediction-Control Tasks Using Temporal Difference Learning Methods

There has been recent interest in using temporal difference learning methods to attack problems of prediction and control. While these algorithms have been brought to bear on many problems, they remain poorly understood. It is the purpose of this thesis to further explore these algorithms, presenting a framework for viewing them and raising a number of practical issues and exploring those issues in the context of several case studies. This includes applying the TD(lambda) algorithm to: 1) learning to play tic-tac-toe from the outcome of self-play and of play against a perfectly-playing opponent and 2) learning simple one-dimensional segmentation tasks.