Simultaneous Discovery of Reusable Detectors

This paper describes an approach for automatically decomposing a problem into subproblems and then automatically discovering reusable subroutines , and a way of assembling the results produced by these subroutines in order to solve a problem. The approach uses g e n e t i c p r o g r a m m i n g w i t h automatic funct ion def init ion. Genetic programming provides a way to genetically breed a computer program to solve a problem. Automatic funct ion def ini t ion enables genetic programming to d e f i n e p o t e n t i a l l y u s e f u l subroutines dynamically during a run. The approach is applied to an illustrative problem. Genetic programming wi th automat ic function definition reduced the computational effort required to learn a solution to the problem by a factor of 2.0 as compared to genetic programming without automatic function definition. Similarly, the average structural complexity of the solution was reduced by about 21%. 1 . INTRODUCTION AND OVERVIEW An important goal of machine learning and artificial intelligence is the discovery of an automatic way to solve problems hierarchica l ly . The hierarchical approach to problemsolving can be viewed a three-step process. In the top-down way of describing this three-step process, one starts with the overall problem and seeks to discover a way to decompose the problem into subproblems. Second, one tries a way to solve each of the presumably simpler subproblems. Third, one seeks a way to assemble the solutions to the subproblems into a solution to the original overall problem. Solving some of the subproblems may require further invocation of this threestep process. If this three-step process is successful , one ends up with a hierarchical solution to the problem. Hierarchical solutions to problems are potentially advantageous for machine learning because they avoid tediously resolving what are essentially identical problems, because hierarchical solutions may be more parsimonious, and because hierarchical solutions may reduce the computational effort involved in doing the machine learning necessary to solve the problem. The acceleration in learning is especially great when it is possible to reuse, with or without modification, the solutions to the subproblems. This acceleration is i m p o r t a n t b e c a u s e p e r f o r m a n c e improvement by means of some kind of hierarchical approach appears to be necessary if machine learning methods are ever to be scaled up from small "proof of principle" problems to large problems. Conventional approaches to machine learning usually require that the user hand-craft reusable subroutines for key features in the problem environment. C o n v e n t i o n a l a p p r o a c h e s o f t e n additionally require the user to specify in advance the size and shape of the eventual way of combining the subroutines into a compete solution. However, in many ins tances , f ind ing the r eusab le subroutines and a way of combining the subroutines in order to solve the problem really is t h e p r o b l e m . Indeed, the necessity for pre-identification of the particular components of solutions and the necessity for pre-determination of a way of combining these components has been recognized as a bane of machine learning starting with Samuel's groundbreaking work in machine learning involving learning to play the game of checkers [Samuel 1959]. In Samuel's checkers player, learning consisted of progressively adjusting numerical coefficients in an algebraic expression of a predetermined functional form (specifically, a polynomial of specified order). Each component term of the polynomial represented a handcrafted detector reflecting some aspect of the current state of the board (e.g., number of pieces, center control, etc.). The polynomial weighted each detector with a numerical coefficient and thereby assigned a single numerical value of a board to the player. If a polynomial were good at assigning values to boards, the polynomial could be used to compare the boards that would arise if the player were to make various alternative moves – thus permitting the best move to be selected from among the alternatives on the basis of the polynomial. In Samuel's learning system, the numerical coefficients of the polynomial were adjusted with experience, so that the predictive quality of the polynomial progress ively improved. Samuel predetermined the way the detectors would be combined to solve the problem by selecting the functional form of the polynomial. Samuel recognized, from the beginning, the importance of enabling learning to occur without predetermining the size and shape of the solution and of "[getting] the program to generate its own parameters (detectors) for the evaluation