Academic

We derive a Berry-Esseen bound for the multivariate normal approximation of the Polyak-Ruppert averaged iterates in the linear stochastic approximation (LSA) algorithm, driven by i.i.d. noise and a decreasing step size. This result is then used to establish the non-asymptotic validity of the multiplier bootstrap procedure for constructing confidence sets in parameter estimation with LSA.

Additionally, we discuss LSA with Markovian noise and extend our results to the case of the Stochastic Gradient Descent algorithm.

This talk is based on joint works with D. Belomestny, E. Moulines, S. Samsonov, M. Sheshukova, Q.-M. Shao, and Z.-S. Zhang.