Proves the first fully non-asymptotic bound on the accuracy of multiplier bootstrap for constructing confidence sets from Polyak-Ruppert SGD iterates, achieving convex-distance rates up to 1/sqrt(n) under regularity conditions.
(54) Using the elementary bound 1 + t ≤ et for any t ∈ R, we get A1,k ≤ exp −(3/2)µ kX i=1 αi exp 2L2 2 kX i=1 α2 i
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Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent
Proves the first fully non-asymptotic bound on the accuracy of multiplier bootstrap for constructing confidence sets from Polyak-Ruppert SGD iterates, achieving convex-distance rates up to 1/sqrt(n) under regularity conditions.