Universal Induction with Varying Sets of Combinators

Abstract: Universal induction is a crucial issue in AGI. Its practical applicability can be achieved by the choice of the reference machine or representation of algorithms agreed with the environment. This machine should be updatable for solving subsequent tasks more efficiently. We study this problem on an example of combinatory logic as the very simple Turing-complete reference machine, which enables modifying program representations by introducing different sets of primitive combinators. Genetic programming system is used to search for combinator expressions, which are easily decomposed into sub-expressions being recombined in crossover. Our experiments show that low-complexity induction or prediction tasks can be solved by the developed system (much more efficiently than using brute force); useful combinators can be revealed and included into the representation simplifying more difficult tasks. However, optimal sets of combinators depend on the specific task, so the reference machine should be adaptively chosen in coordination with the search engine.