An unbounded Berge´s minimum theorem with applications to discounted Markov decision processes

Title:

An unbounded Berge´s minimum theorem with applications to discounted Markov decision processes

Creator:

Montes-de-Oca, Raúl and Lemus-Rodríguez, Enrique

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:b7423769-f5a1-4051-a78f-c049a38bb4df
uuid:b7423769-f5a1-4051-a78f-c049a38bb4df

Subject:

Berge´s minimum theorem, moment function, discounted Markov decision process, uniqueness of the optimal policy, and continuous optimal policy

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

This paper deals with a certain class of unbounded optimization problems. The optimization problems taken into account depend on a parameter. Firstly, there are established conditions which permit to guarantee the continuity with respect to the parameter of the minimum of the optimization problems under consideration, and the upper semicontinuity of the multifunction which applies each parameter into its set of minimizers. Besides, with the additional condition of uniqueness of the minimizer, its continuity is given. Some examples of nonconvex optimization problems that satisfy the conditions of the article are supplied. Secondly, the theory developed is applied to discounted Markov decision processes with unbounded cost functions and with possibly noncompact actions sets in order to obtain continuous optimal policies. This part of the paper is illustrated with two examples of the controlled Lindley's random walk. One of these examples has nonconstant action sets.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[268]-286

Source:

Kybernetika | 2012 Volume:48 | Number:2

Harvested from:

CDK

Metadata only:

false