17584

Автор(ы): 

Автор(ов): 

2

Параметры публикации

Тип публикации: 

Доклад

Название: 

The Mirror Descent Control Algorithm for Weakly Regular Homogeneous Finite Markov Chains with Unknown Mean Losses

Электронная публикация: 

Да

ISBN/ISSN: 

0743-1546

Наименование конференции: 

  • 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC-2011, Orlando, Fl)

Наименование источника: 

  • Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC-2011, Orlando, Fl)

Город: 

  • Орландо, США

Издательство: 

  • Institute of Electrical and Electronics Engineers (IEEE)

Год издания: 

2011

Страницы: 

1779-1783
Аннотация
We address the adaptive stochastic control problem for a discrete time system described by controlled Markov chain with finite number of states. The mirror descent randomized control algorithm on the class of controlled homogeneous finite Markov chains with unknown mean losses has been proposed and studied. Here we develop the approach represented in Nazin and Miller (2011). The main assumptions are the following: processes are independent and stationary, nonnegative random losses are almost surely bounded by a given constant, and the connectivity assumption for the controlled Markov chain holds. The uncertainty is that the mean loss matrix is unknown. The novelty of the approach is in extension of the class of controlled homogeneous finite Markov chains to the chains with connectivity assumption. The main result consists in demonstration of the asymptotical upper bound as the time tends to infinity and in determining of the explicit constant which is weakly depending on the logarithm of the number of states.

Библиографическая ссылка: 

Назин А.В., Миллер Б.М. The Mirror Descent Control Algorithm for Weakly Regular Homogeneous Finite Markov Chains with Unknown Mean Losses / Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC-2011, Orlando, Fl). Орландо, США: Institute of Electrical and Electronics Engineers (IEEE), 2011. С. 1779-1783.