A Selective Macro-learning Algorithm and its Application to the NxN Sliding-Tile Puzzle

TL;DR

This paper introduces a selective macro-learning algorithm that acquires useful macros to improve problem-solving efficiency, demonstrated on NxN sliding-tile puzzles, enabling solutions for larger puzzles after training on smaller ones.

Contribution

A general method for selective macro acquisition that improves problem-solving efficiency by focusing on macros that escape local minima.

Findings

Macros acquired are effective in solving larger puzzles.

The method reduces search complexity in NxN sliding-tile puzzles.

System generalizes from small to large puzzle sizes.

Abstract

One of the most common mechanisms used for speeding up problem solvers is macro-learning. Macros are sequences of basic operators acquired during problem solving. Macros are used by the problem solver as if they were basic operators. The major problem that macro-learning presents is the vast number of macros that are available for acquisition. Macros increase the branching factor of the search space and can severely degrade problem-solving efficiency. To make macro learning useful, a program must be selective in acquiring and utilizing macros. This paper describes a general method for selective acquisition of macros. Solvable training problems are generated in increasing order of difficulty. The only macros acquired are those that take the problem solver out of a local minimum to a better state. The utility of the method is demonstrated in several domains, including the domain of NxN sliding-tile puzzles. After learning on small puzzles, the system is able to efficiently solve puzzles of any size.