[ARTICLE] This paper introduces a class of Markov chains encompassing models of stochastic approximation, both averaging and non-averaging. Using a martingale approximation method, it establishes deviation inequalities for separately Lipschitz functions of the chain under various moment conditions.

by Pierre ALQUIER (ESSEC Business School),  Xiequan FAN, Paul DOUKHAN

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.

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