A Version of Geiringer-like Theorem for Decision Making in the Environments with Randomness and Incomplete Information

Purpose – The purpose of this paper is to establish a version of a theorem that originated from population genetics and has been later adopted in evolutionary computation theory that will lead to novel Monte-Carlo sampling algorithms that provably increase the AI potential. Design/methodology/approach – In the current paper the authors set up a mathematical framework, state and prove a version of a Geiringer-like theorem that is very well-suited for the development of Mote-Carlo sampling algorithms to cope with randomness and incomplete information to make decisions. Findings – This work establishes an important theoretical link between classical population genetics, evolutionary computation theory and model free reinforcement learning methodology. Not only may the theory explain the success of the currently existing Monte-Carlo tree sampling methodology, but it also leads to the development of novel Monte-Carlo sampling techniques guided by rigorous mathematical foundation. Practical implications – The theoretical foundations established in the current work provide guidance for the design of powerful Monte-Carlo sampling algorithms in model free reinforcement learning, to tackle numerous problems in computational intelligence. Originality/value – Establishing a Geiringer-like theorem with non-homologous recombination was a long-standing open problem in evolutionary computation theory. Apart from overcoming this challenge, in a mathematically elegant fashion and establishing a rather general and powerful version of the theorem, this work leads directly to the development of novel provably powerful algorithms for decision making in the environment involving randomness, hidden or incomplete information.