TY - JOUR
T1 - Markov games with unknown random state-actions-dependent discount factors
T2 - Empirical estimation
AU - González-Sánchez, David
AU - Luque-Vásquez, Fernando
AU - Minjárez-Sosa, Jesus Adolfo
N1 - Publisher Copyright:
© 2019 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
PY - 2019/1/1
Y1 - 2019/1/1
N2 - The work deals with a class of discrete-time zero-sum Markov games under a discounted optimality criterion with random state-action-dependent discount factors of the form (Formula presented.), where xn,an,bn, and ξn+1 are the state, the actions of players, and a random disturbance at time n, respectively, taking values in Borel spaces. The one-stage payoff is assumed to be possibly unbounded. In addition, the process {ξn} is formed by observable, independent, and identically distributed random variables with common distribution θ, which is unknown to players. By using the empirical distribution to estimate θ, we introduce a procedure to approximate the value V∗ of the game; such a procedure yields construction schemes of stationary optimal strategies and asymptotically optimal Markov strategies.
AB - The work deals with a class of discrete-time zero-sum Markov games under a discounted optimality criterion with random state-action-dependent discount factors of the form (Formula presented.), where xn,an,bn, and ξn+1 are the state, the actions of players, and a random disturbance at time n, respectively, taking values in Borel spaces. The one-stage payoff is assumed to be possibly unbounded. In addition, the process {ξn} is formed by observable, independent, and identically distributed random variables with common distribution θ, which is unknown to players. By using the empirical distribution to estimate θ, we introduce a procedure to approximate the value V∗ of the game; such a procedure yields construction schemes of stationary optimal strategies and asymptotically optimal Markov strategies.
KW - discounted optimality
KW - empirical estimation
KW - markov games
KW - non-constant discount factors
UR - http://www.scopus.com/inward/record.url?scp=85070753459&partnerID=8YFLogxK
U2 - 10.1002/asjc.2159
DO - 10.1002/asjc.2159
M3 - Artículo
AN - SCOPUS:85070753459
SN - 1561-8625
VL - 23
SP - 166
EP - 177
JO - Asian Journal of Control
JF - Asian Journal of Control
IS - 1
ER -