The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 14, Number 2 (2004), 796-819.
Convergence rate of linear two-time-scale stochastic approximation
We study the rate of convergence of linear two-time-scale stochastic approximation methods. We consider two-time-scale linear iterations driven by i.i.d. noise, prove some results on their asymptotic covariance and establish asymptotic normality. The well-known result [Polyak, B. T. (1990). Automat. Remote Contr. 51 937–946; Ruppert, D. (1988). Technical Report 781, Cornell Univ. ] on the optimality of Polyak–Ruppert averaging techniques specialized to linear stochastic approximation is established as a consequence of the general results in this paper.
Ann. Appl. Probab., Volume 14, Number 2 (2004), 796-819.
First available in Project Euclid: 23 April 2004
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Primary: 62L20: Stochastic approximation
Konda, Vijay R.; Tsitsiklis, John N. Convergence rate of linear two-time-scale stochastic approximation. Ann. Appl. Probab. 14 (2004), no. 2, 796--819. doi:10.1214/105051604000000116. https://projecteuclid.org/euclid.aoap/1082737112