ALQUIER Pierre, FAN Xiequan, DOUKHAN Paul
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.
FAN, X., ALQUIER, P. et DOUKHAN, P. (2022). Deviation inequalities for stochastic approximation by averaging. Stochastic Processes and their Applications, 152, pp. 452-485.