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arXiv · 2102.08685

Deviation inequalities for stochastic approximation by averaging

Xiequan Fan·Pierre Alquier·Paul Doukhan
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Abstract

We introduce a class of Markov chains, that contains the model of stochastic approximation by averaging and non-averaging. Using 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 the stochastic approximation by averaging and empirical risk minimisation.

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Xiequan Fan, Pierre Alquier, Paul Doukhan. 2021-02-17. Deviation inequalities for stochastic approximation by averaging. https://doi.org/10.1016/j.spa.2022.07.002

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