Work

Maximizing the probability of visiting a set infinitely often for a Markov decision process with Borel state and action spaces

Year: 2024

Type: article

Abstract: We consider a Markov control model with Borel state space, metric compact action space, and transitions assumed to have a density function with respect to some probability measure satisfying some continuity conditions. We study the optimization problem of maximizing the probability of visiting some subset of the state space infinitely often, and we show that there exists an optimal stationary Markov policy for this problem. We endow the set of stationary Markov policies and the family of strategic probability measures with adequate topologies (namely, the narrow topology for Young measures and the $ws^\infty$ -topology, respectively) to obtain compactness and continuity properties, which allow us to obtain our main results.

Source: Journal of Applied Probability

DOI: 10.1017/jpr.2024.25

Authors: François Dufour, Tomás Prieto-Rumeau

Institutions: Institut Polytechnique de Bordeaux, Universidad Nacional de Educación a Distancia

Language: English

Topic: Adaptive Dynamic Programming Control

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funder: Ministerio de Ciencia e Innovación