A Formal Framework for Speedup Learning from Problems and Solutions

TL;DR

This paper introduces a formal framework for speedup learning from problems and solutions, unifying various learning approaches and demonstrating their effectiveness through implementations in symbolic integration and the Eight Puzzle.

Contribution

It develops a comprehensive formal framework that encompasses empirical and explanation-based speedup learning, with constructive proofs and algorithms for control rules and macro-operators.

Findings

Framework captures both empirical and explanation-based speedup learning

Provides constructive proofs with learning algorithms for different representations

Demonstrates effectiveness in symbolic integration and Eight Puzzle domains

Abstract

Speedup learning seeks to improve the computational efficiency of problem solving with experience. In this paper, we develop a formal framework for learning efficient problem solving from random problems and their solutions. We apply this framework to two different representations of learned knowledge, namely control rules and macro-operators, and prove theorems that identify sufficient conditions for learning in each representation. Our proofs are constructive in that they are accompanied with learning algorithms. Our framework captures both empirical and explanation-based speedup learning in a unified fashion. We illustrate our framework with implementations in two domains: symbolic integration and Eight Puzzle. This work integrates many strands of experimental and theoretical work in machine learning, including empirical learning of control rules, macro-operator learning, Explanation-Based Learning (EBL), and Probably Approximately Correct (PAC) Learning.