| Title:
|
Approximation and estimation in Markov control processes under a discounted criterion (English) |
| Author:
|
Minjárez-Sosa, J. Adolfo |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
40 |
| Issue:
|
6 |
| Year:
|
2004 |
| Pages:
|
[681]-690 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a class of discrete-time Markov control processes with Borel state and action spaces, and $\Re ^{k}$-valued i.i.d. disturbances with unknown density $\rho .$ Supposing possibly unbounded costs, we combine suitable density estimation methods of $\rho $ with approximation procedures of the optimal cost function, to show the existence of a sequence $\lbrace \hat{f}_{t}\rbrace $ of minimizers converging to an optimal stationary policy $f_{\infty }.$ (English) |
| Keyword:
|
Markov control processes |
| Keyword:
|
density estimation |
| Keyword:
|
discounted cost criterion |
| MSC:
|
90B05 |
| MSC:
|
90B30 |
| MSC:
|
90C40 |
| MSC:
|
93E10 |
| idZBL:
|
Zbl 1249.93163 |
| idMR:
|
MR2120390 |
| . |
| Date available:
|
2009-09-24T20:05:08Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135626 |
| . |
| Reference:
|
[1] Cavazos-Cadena R.: Nonparametric adaptive control of discounted stochastic systems with compact state space.J. Optim. Theory Appl. 65 (1990), 191–207 Zbl 0699.93053, MR 1051545, 10.1007/BF01102341 |
| Reference:
|
[2] Devroye L., Gyorfi L.: Nonparametric Density Estimation the $L_{1}$ View.Wiley, New York 1985 MR 0780746 |
| Reference:
|
[3] Dynkin E. B., Yushkevich A. A.: Controlled Markov Processes.Springer–Verlag, New York 1979 MR 0554083 |
| Reference:
|
[4] Gordienko E. I.: Adaptive strategies for certain classes of controlled Markov processes.Theory Probab. Appl. 29 (1985), 504–518 Zbl 0577.93067 |
| Reference:
|
[5] Gordienko E. I., Minjárez-Sosa J. A.: Adaptive control for discrete-time Markov processes with unbounded costs: discounted criterion.Kybernetika 34 (1998), 217–234 MR 1621512 |
| Reference:
|
[6] Hasminskii R., Ibragimov I.: On density estimation in the view of Kolmogorov’s ideas in approximation theory.Ann. Statist. 18 (1990), 999–1010 Zbl 0705.62039, MR 1062695, 10.1214/aos/1176347736 |
| Reference:
|
[7] Hernández-Lerma O.: Adaptive Markov Control Processes.Springer–Verlag, New York 1989 MR 0995463 |
| Reference:
|
[8] Hernández-Lerma O., Cavazos-Cadena R.: Density estimation and adaptive control of Markov processes: average and discounted criteria.Acta Appl. Math. 20 (1990), 285–307 MR 1081591, 10.1007/BF00049572 |
| Reference:
|
[9] Hernández-Lerma O., Lasserre J. B.: Discrete-Time Markov Control Processes: Basic Optimality Criteria.Springer–Verlag, New York 1996 Zbl 0840.93001, MR 1363487 |
| Reference:
|
[10] Hernández-Lerma O., Lasserre J. B.: Further Topics on Discrete-Time Markov Control Processes.Springer–Verlag, New York 1999 Zbl 0928.93002, MR 1697198 |
| Reference:
|
[11] Hernández-Lerma O., Marcus S. I.: Adaptive policies for discrete-time stochastic control systems with unknown disturbance distribution.Systems Control Lett. 9 (1987), 307–315 Zbl 0637.93075, MR 0912683, 10.1016/0167-6911(87)90055-7 |
| Reference:
|
[12] Hilgert N., Minjárez-Sosa J. A.: Adaptive policies for time-varying stochastic systems under discounted criterion.Math. Methods Oper. Res. 54 (2001), 491–505 Zbl 1042.93065, MR 1890916, 10.1007/s001860100170 |
| Reference:
|
[13] Schäl M.: Conditions for optimality and for the limit of $n$-stage optimal policies to be optimal.Z. Wahrs. Verw. Gerb. 32 (1975), 179–196 MR 0378841, 10.1007/BF00532612 |
| . |
