4 papers
Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent
Marina Sheshukova, Sergey Samsonov, Denis Belomestny +4
In this paper, we establish the non-asymptotic validity of the multiplier bootstrap procedure for constructing the confidence sets using the Stochastic Gradient Descent (SGD) algor…
Refined Berry-Esseen bounds under local dependence
Zhi-Jun Cai, Qi-Man Shao, Zhuo-Song Zhang
In this paper, we establish Berry--Esseen bounds for both self-normalized and non-self-normalized sums of locally dependent random variables. The proofs are based on Stein's method…
Improved Central Limit Theorem and Bootstrap Approximations for Linear Stochastic Approximation
Bogdan Butyrin, Eric Moulines, Alexey Naumov +3
In this paper, we refine the Berry-Esseen bounds for the multivariate normal approximation of Polyak-Ruppert averaged iterates arising from the linear stochastic approximation (LSA…
Gaussian Approximation and Multiplier Bootstrap for Polyak-Ruppert Averaged Linear Stochastic Approximation with Applications to TD Learning
Sergey Samsonov, Eric Moulines, Qi-Man Shao +2
In this paper, we obtain the Berry-Esseen bound for multivariate normal approximation for the Polyak-Ruppert averaged iterates of the linear stochastic approximation (LSA) algorith…