TY - JOUR
T1 - LP based upper and lower bounds for Cesàro and Abel limits of the optimal values in problems of control of stochastic discrete time systems
AU - Avrachenkov, Konstantin
AU - Gaitsgory, Vladimir
AU - Gamertsfelder, Lucas
PY - 2022/8/1
Y1 - 2022/8/1
N2 - In this paper, we study asymptotic properties of problems of control of stochastic discrete time systems (also known as Markov decision processes) with time averaging and time discounting optimality criteria, and we establish that the Cesàro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-dimensional linear programming problem and its dual.
AB - In this paper, we study asymptotic properties of problems of control of stochastic discrete time systems (also known as Markov decision processes) with time averaging and time discounting optimality criteria, and we establish that the Cesàro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-dimensional linear programming problem and its dual.
KW - Stochastic optimal control
KW - Markov decision processes (MDPs)
KW - Linear programming
KW - Optimality conditions
KW - Dynamic programming
KW - Discrete time
UR - http://www.scopus.com/inward/record.url?scp=85125667194&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2022.126121
DO - 10.1016/j.jmaa.2022.126121
M3 - Article
AN - SCOPUS:85125667194
SN - 0022-247X
VL - 512
SP - 1
EP - 54
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 126121
ER -