4 research outputs found
A Formal Framework for Speedup Learning from Problems and Solutions
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.Comment: See http://www.jair.org/ for any accompanying file
A Selective Macro-learning Algorithm and its Application to the NxN Sliding-Tile Puzzle
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.Comment: See http://www.jair.org/ for an online appendix and other files
accompanying this articl
A Formalization of Explanation-Based Macro-operator Learning
In spite of the popularity of Explanation-Based Learning (EBL), its theoretical basis is not well-understood. Using a generalization of Probably Approximately Correct (PAC) learning to problem solving domains, this paper formalizes two forms of Explanation-Based Learning of macro-operators and proves the sufficient conditions for their success. These two forms of EBL, called "Macro Caching " and "Serial Parsing," respectively exhibit two distinct sources of power or "bias": the sparseness of the solution space and the decomposability of the problem-space. The analysis shows that exponential speedup can be achieved when either of these biases is suitable for a domain. Somewhat surprisingly, it also shows that computing the preconditions of the macro-operators is not necessary to obtain these speedups. The theoretical results are confirmed by experiments in the domain of Eight Puzzle. Our work suggests that the best way to address the utility problem in EBL is to implement a bias which exploits the problem-space structure of the set of domains that one is interested in learning.
A Formalization of Explanation-Based Macro-operator Learning
In spite of the popularity of Explanation-Based Learning (EBL), its theoretical basis is not well-understood. Using a generalization of Probably Approximately Correct (PAC) learning to problem solving domains, this paper formalizes two forms of Explanation-Based Learning of macro-operators and proves the sufficient conditions for their success. These two forms of EBL, called "Macro Caching" and "Serial Parsing, " respectively exhibit two distinct sources of power or "bias": the sparseness of the solution space and the decomposability of the problem-space. The analysis shows that exponential speedup can be achieved when either of these biases is suitable for a domain. Somewhat surprisingly, it also shows that computing the preconditions of the macro-operators is not necessary to obtain these speedups. The theoretical results are confirmed by experiments in the domain of Eight Puzzle. Our work suggests that the best way to address the utility problem in EBL is to implement a bias which e..