Deviation inequalities for stochastic approximation by averaging
This work provides theoretical guarantees for stochastic approximation methods, which is incremental as it extends existing analysis to more general settings.
The paper tackles the problem of establishing deviation inequalities for stochastic approximation algorithms by introducing a class of Markov chains and using martingale approximation methods, resulting in theoretical bounds applied to stochastic approximation by averaging and empirical risk minimization.
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.