A Further Generalization of the Finite-Population Geiringer-like Theorem for POMDPs to Allow Recombination Over Arbitrary Set Covers
This work provides an incremental improvement for researchers in AI and decision-making under uncertainty, allowing broader application of recombination methods in POMDPs.
The paper tackles the limitation of requiring equivalence relations for similarity in a finite-population Geiringer-like theorem for POMDPs, by generalizing it to allow arbitrary set covers for state-action pairs, enabling more flexible modeling of uncertainty and incomplete information in Monte-Carlo tree search.
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.