Deviation inequalities for stochastic approximation by averaging

Xiequan Fan, Pierre Alquier and Paul Doukhan

Stochastic Processes and their Applications, 2022, vol. 152, issue C, 452-485

Abstract: We introduce a class of Markov chains that includes models of stochastic approximation by averaging and non-averaging. Using a martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions of such a chain, with different moment conditions on some dominating random variables of martingale differences. Finally, we apply these inequalities to stochastic approximation by averaging and empirical risk minimization.

Keywords: Deviation inequalities; Martingales; Iterated random functions; Stochastic approximation by averaging; Empirical risk minimization (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.07.002

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