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.

翻译：我们引入了一组马可夫链条,它包含平均和非平均的随机近似模型。 我们使用马丁加勒近近似法为这种链条的单独利普施奇茨功能设定了不同的偏差不平等,而某些随机的马丁加尔差变数则条件不同。 最后,我们通过平均和实证风险最小化,将这些不平等运用到随机近近似中。