# Optimal non-asymptotic bound of the Ruppert-Polyak averaging without strong convexity

@article{Gadat2017OptimalNB, title={Optimal non-asymptotic bound of the Ruppert-Polyak averaging without strong convexity}, author={S{\'e}bastien Gadat and Fabien Panloup}, journal={arXiv: Statistics Theory}, year={2017} }

This paper is devoted to the non-asymptotic control of the mean-squared error for the Ruppert-Polyak stochastic averaged gradient descent introduced in the seminal contributions of [Rup88] and [PJ92]. In our main results, we establish non-asymptotic tight bounds (optimal with respect to the Cramer-Rao lower bound) in a very general framework that includes the uniformly strongly convex case as well as the one where the function f to be minimized satisfies a weaker Kurdyka-Lojiasewicz-type…

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