Geodesic
Multivariate compact law of the iterated logarithm for averaged stochastic approximation algorithms
Serdica Mathematical Journal, Tome 46 (2021) no. 4, pp. 335-356.

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The aim of this paper is to establish a multivariate compact law of the iterated logarithm for the averaged version of stochastic approximation algorithms. This is achieved by studying the strong convergence rate of a two-time-scale stochastic approximation algorithm, the use of which generalizes the averaging principle of stochastic approximation algorithms. The general result obtained is then applied to the well-known averaged versions of Robbins-Monro's and Kiefer-Wolfowitz's algorithms.
Keywords: stochastic approximation algorithm, averaging principle, strong convergence rate, 62L20, 60F05, 62G07 
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     title = {Multivariate compact law of the iterated logarithm for averaged stochastic approximation algorithms},
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Mokkadem, Abdelkader; Pelletier, Mariane. Multivariate compact law of the iterated logarithm for averaged stochastic approximation algorithms. Serdica Mathematical Journal, Tome 46 (2021) no. 4, pp. 335-356. http://geodesic.mathdoc.fr/item/SMJ2_2021_46_4_a2/