Title :
Asymptotic properties of two time-scale stochastic approximation algorithms with constant step sizes
Author :
Tadic, Vladislav B. ; Meyn, Sean P.
Author_Institution :
Dept. of Electr. & Electron. Eng., Melbourne Univ., Parkville, Vic., Australia
Abstract :
Asymptotic properties of two time-scale stochastic approximation algorithms with constant step sizes are analyzed in this paper. The analysis is carried out for the algorithms with additive noise, as well as for the algorithms with non-additive noise. The algorithms with additive noise are considered for the case where the noise id state-dependent and admits the decomposition as a sum of a martingale difference sequence and a telescoping sequence. The algorithms with non-additive noise are analyzed for the case where the noise satisfies uniform or strong mixing conditions, as well as for the case where the noise is a Markov chain controlled by the algorithm states.
Keywords :
Markov processes; approximation theory; noise; sequences; Markov chain; additive noise; algorithm states; asymptotic properties; constant step sizes; martingale difference sequence; nonadditive noise; state dependent noise; telescoping sequence; two time scale stochastic approximation algorithms; Additive noise; Algorithm design and analysis; Approximation algorithms; Communication networks; Machine learning; Machine learning algorithms; Signal processing algorithms; Size control; Stochastic processes; Stochastic resonance;
Conference_Titel :
American Control Conference, 2003. Proceedings of the 2003
Print_ISBN :
0-7803-7896-2
DOI :
10.1109/ACC.2003.1240536
