A Moreau-Yosida regularization for Markov decision processes

Abstract This paper addresses a class of sequential optimization problems known as Markov decision processes. These kinds of processes are considered on Euclidean state and action spaces with the total expected discounted cost as the objective function. The main goal of the paper is to provide condi...

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Autores principales:	Ortega-Gutiérrez,R. Israel, Cruz-Suárez,Hugo
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2021
Materias:	Discounted Markov decision processes Uniqueness of optimal policies, Moreau-Yosida regularization
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000100117
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spelling	oai:scielo:S0716-091720210001001172021-01-26A Moreau-Yosida regularization for Markov decision processesOrtega-Gutiérrez,R. IsraelCruz-Suárez,Hugo Discounted Markov decision processes Uniqueness of optimal policies, Moreau-Yosida regularization Abstract This paper addresses a class of sequential optimization problems known as Markov decision processes. These kinds of processes are considered on Euclidean state and action spaces with the total expected discounted cost as the objective function. The main goal of the paper is to provide conditions to guarantee an adequate Moreau-Yosida regularization for Markov decision processes (named the original process). In this way, a new Markov decision process that conforms to the Markov control model of the original process except for the cost function induced via the Moreau-Yosida regularization is established. Compared to the original process, this new discounted Markov decision process has richer properties, such as the differentiability of its optimal value function, strictly convexity of the value function, uniqueness of optimal policy, and the optimal value function and the optimal policy of both processes, are the same. To complement the theory presented, an example is provided.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.1 20212021-02-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000100117en10.22199/issn.0717-6279-2021-01-0008
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Discounted Markov decision processes Uniqueness of optimal policies, Moreau-Yosida regularization
spellingShingle	Discounted Markov decision processes Uniqueness of optimal policies, Moreau-Yosida regularization Ortega-Gutiérrez,R. Israel Cruz-Suárez,Hugo A Moreau-Yosida regularization for Markov decision processes
description	Abstract This paper addresses a class of sequential optimization problems known as Markov decision processes. These kinds of processes are considered on Euclidean state and action spaces with the total expected discounted cost as the objective function. The main goal of the paper is to provide conditions to guarantee an adequate Moreau-Yosida regularization for Markov decision processes (named the original process). In this way, a new Markov decision process that conforms to the Markov control model of the original process except for the cost function induced via the Moreau-Yosida regularization is established. Compared to the original process, this new discounted Markov decision process has richer properties, such as the differentiability of its optimal value function, strictly convexity of the value function, uniqueness of optimal policy, and the optimal value function and the optimal policy of both processes, are the same. To complement the theory presented, an example is provided.
author	Ortega-Gutiérrez,R. Israel Cruz-Suárez,Hugo
author_facet	Ortega-Gutiérrez,R. Israel Cruz-Suárez,Hugo
author_sort	Ortega-Gutiérrez,R. Israel
title	A Moreau-Yosida regularization for Markov decision processes
title_short	A Moreau-Yosida regularization for Markov decision processes
title_full	A Moreau-Yosida regularization for Markov decision processes
title_fullStr	A Moreau-Yosida regularization for Markov decision processes
title_full_unstemmed	A Moreau-Yosida regularization for Markov decision processes
title_sort	moreau-yosida regularization for markov decision processes
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000100117
work_keys_str_mv	AT ortegagutierrezrisrael amoreauyosidaregularizationformarkovdecisionprocesses AT cruzsuarezhugo amoreauyosidaregularizationformarkovdecisionprocesses AT ortegagutierrezrisrael moreauyosidaregularizationformarkovdecisionprocesses AT cruzsuarezhugo moreauyosidaregularizationformarkovdecisionprocesses
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A Moreau-Yosida regularization for Markov decision processes

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