A Further Generalization of the Finite-Population Geiringer-like Theorem for POMDPs to Allow Recombination Over Arbitrary Set Covers

TL;DR

This paper extends the finite-population Geiringer-like theorem for POMDPs, allowing for more flexible similarity relations modeled by arbitrary set covers, enhancing Monte-Carlo tree search in uncertain environments.

Contribution

It generalizes the theorem by replacing the equivalence relation with arbitrary set covers, broadening its applicability in POMDPs and Monte-Carlo methods.

Findings

The theorem now accommodates arbitrary set covers for similarity.

Enhanced Monte-Carlo tree search in POMDPs with complex state similarities.

Broader applicability in uncertain and incomplete information environments.

Abstract

A popular current research trend deals with expanding the Monte-Carlo tree search sampling methodologies to the environments with uncertainty and incomplete information. Recently a finite population version of Geiringer theorem with nonhomologous recombination has been adopted to the setting of Monte-Carlo tree search to cope with randomness and incomplete information by exploiting the entrinsic similarities within the state space of the problem. The only limitation of the new theorem is that the similarity relation was assumed to be an equivalence relation on the set of states. In the current paper we lift this "curtain of limitation" by allowing the similarity relation to be modeled in terms of an arbitrary set cover of the set of state-action pairs.