Extending Explanation-Based Learning by Generalizing the Structure of Explanations

Preface and Acknowledgments1 Introduction 1.1 The Need for Generalizing Explanation Structures 1.2 Overview of this Book 1.2.1 Chapter Summaries 1.2.2 Relevance to Research Areas Outside Machine Learning 1.3 Explanation-Based Learning 1.3.1 A Brief History 1.3.2 The Standard Method 1.3.3 Additional Research Issues2 Learning in Mathematically-Based Domains 2.1 The PHYSICS 101 System 2.1.1 The Learning Model 2.1.2 Terminology 2.1.3 Other Approaches to Learning in Mathematical Domains 2.2 Solving Problems 2.2.1 Initial Knowledge of the System 2.2.2 Schema-Based Problem Solving 2.2.3 Choosing the Initial Equation 2.2.4 Transforming an Expression into an Acceptable Form 2.3 Building Explanations 2.2.1 A Sample Problem 2.3.2 Verifying a Teacher's Solution 2.3.3 Explaining Solutions 2.3.4 Understanding Obstacles 2.3.5 Constructing the Cancellation Graph — Algorithmic Details 2.4 Generalizing Solutions 2.4.1 The Result of Standard Explanation-Based Learning 2.4.2 Using the Cancellation Graph to Guide Generalization 2.4.3 Learning Special-Case Schemata 2.4.4 Performance Analysis 2.5 Summary3 A Domain-Independent Approach 3.1 The BAGGER System 3.1.1 Some Sample Learning Episodes 3.1.2 Situation Calculus 3.1.3 Sequential Rules 3.1.4 Representing Sequential Knowledge 3.2 Generalizing 3.2.1 The BAGGER Generalization Algorithm 3.2.2 Problem Solving in BAGGER 3.2.3 Simplifying the Antecedents in Sequential Rules 3.2.4 Two Examples 3.3 Extending BAGGER 3.3.1 Algorithmic Details and Correctness Proof 3.3.2 The Circuit Implementation Domain Revisited 3.3.3 Learning from Multiple Examples 3.3.4 Problem Solving with Rules Acquired by BAGGER2 3.3.5 Improving the Efficiency of the Rules BAGGER2 Learns 3.3.6 Learning About Wagons 3.3.7 Comparing BAGGER and BAGGER2 114 3.4 Summary4 An Empirical Analysis of Explanation-Based Learning 4.1 Introduction 4.2 Experimental Methodology 4.3 Experiments 4.3.1 Comparison of the Two Training Strategies 4.3.2 Effect of Increased Problem Complexity 4.3.3 Operationality Versus Generality 4.3.4 Time Spent Learning 4.3.5 Clearing Blocks 4.3.6 Rule Access Strategies 4.3.7 Estimating the Performance of the Non-Learning System 4.3.8 Empirical Study of BAGGER2 4.4 Discussion5 Conclusion 5.1 Contributions 5.2 Relation to Other Work 5.2.1 Other Explanation-Based Approaches 5.2.2 Related Work in Similarity-Based Learning 5.2.3 Related Work in Automatic Programming 5.3 Some Open Research Issues 5.3.1 Deciding When to Learn 5.3.2 Improving What is Learned 5.3.3 Extending What can be Learned 5.3.4 Additional Issues 5.4 Final SummaryAppendix A Additional PHYSICS 101 Examples A.1 Overview A.2 Learning About Energy Conservation A.3 Learning About the Sum of Internal Forces A.4 Using the New Force Law to Learn About Momentum A.5 Attempting to Learn from a Two-Ball CollisionAppendix B Additional BAGGER Examples B.1 Overview B.2 More Tower-Building Rules B.3 Clearing an Object B.4 Setting TableAppendix C BAGGER'S Initial Inference Rules C.1 Notation C.2 RulesAppendix D Statistics from Experiments D.1 Description D.2 StatisticsReferences