Empirical approximation in markov games under unbounded payoff: Discounted and average criteria

Fernando Luque-Vásquez; J. Adolfo Minjárez-Sosa

doi:10.14736/kyb-2017-4-0694

Empirical approximation in markov games under unbounded payoff: Discounted and average criteria

Fernando Luque-Vásquez, J. Adolfo Minjárez-Sosa

Departamento de Matemáticas

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

This work deals with a class of discrete-time zero-sum Markov games whose state process fxtg evolves according to the equation xt+1 = F(xt; at; bt; ϵt); where at and bt represent the actions of player 1 and 2, respectively, and {ϵt} is a sequence of independent and identically distributed random variables with unknown distribution θ: Assuming possibly unbounded payo θ, and using the empirical distribution to estimate θ; we introduce approximation schemes for the value of the game as well as for optimal strategies considering both, discounted and average criteria.

Original language	English
Pages (from-to)	694-716
Number of pages	23
Journal	Kybernetika
Volume	53
Issue number	4
DOIs	https://doi.org/10.14736/kyb-2017-4-0694
State	Published - 2017

Bibliographical note

Funding Information:
This work was partially supported by Consejo Nacional de Ciencia y Tecnología (CONACYT) under grant CB2015/254306.

Keywords

Discounted and average criteria
Empirical estimation
Markov games

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10.14736/kyb-2017-4-0694

Cite this

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abstract = "This work deals with a class of discrete-time zero-sum Markov games whose state process fxtg evolves according to the equation xt+1 = F(xt; at; bt; ϵt); where at and bt represent the actions of player 1 and 2, respectively, and {ϵt} is a sequence of independent and identically distributed random variables with unknown distribution θ: Assuming possibly unbounded payo θ, and using the empirical distribution to estimate θ; we introduce approximation schemes for the value of the game as well as for optimal strategies considering both, discounted and average criteria.",

keywords = "Discounted and average criteria, Empirical estimation, Markov games",

author = "Fernando Luque-V{\'a}squez and Minj{\'a}rez-Sosa, {J. Adolfo}",

note = "Funding Information: This work was partially supported by Consejo Nacional de Ciencia y Tecnolog{\'i}a (CONACYT) under grant CB2015/254306.",

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T1 - Empirical approximation in markov games under unbounded payoff

T2 - Discounted and average criteria

AU - Luque-Vásquez, Fernando

AU - Minjárez-Sosa, J. Adolfo

N1 - Funding Information: This work was partially supported by Consejo Nacional de Ciencia y Tecnología (CONACYT) under grant CB2015/254306.

PY - 2017

Y1 - 2017

N2 - This work deals with a class of discrete-time zero-sum Markov games whose state process fxtg evolves according to the equation xt+1 = F(xt; at; bt; ϵt); where at and bt represent the actions of player 1 and 2, respectively, and {ϵt} is a sequence of independent and identically distributed random variables with unknown distribution θ: Assuming possibly unbounded payo θ, and using the empirical distribution to estimate θ; we introduce approximation schemes for the value of the game as well as for optimal strategies considering both, discounted and average criteria.

AB - This work deals with a class of discrete-time zero-sum Markov games whose state process fxtg evolves according to the equation xt+1 = F(xt; at; bt; ϵt); where at and bt represent the actions of player 1 and 2, respectively, and {ϵt} is a sequence of independent and identically distributed random variables with unknown distribution θ: Assuming possibly unbounded payo θ, and using the empirical distribution to estimate θ; we introduce approximation schemes for the value of the game as well as for optimal strategies considering both, discounted and average criteria.

KW - Discounted and average criteria

KW - Empirical estimation

KW - Markov games

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DO - 10.14736/kyb-2017-4-0694

M3 - Artículo

SN - 0023-5954

VL - 53

SP - 694

EP - 716

JO - Kybernetika

JF - Kybernetika

IS - 4

ER -

Empirical approximation in markov games under unbounded payoff: Discounted and average criteria

Abstract

Bibliographical note

Keywords

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