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This paper is devoted to the non-asymptotic control of the mean-squared errorfor the Ruppert-Polyak stochastic averaged gradient descent introduced in theseminal contributions of [Rup88] and [PJ92]. In our main results, we establishnon-asymptotic tight bounds (optimal with respect to the Cramer-Rao lowerbound) in a very general framework that includes the uniformly strongly convexcase as well as the one where the function f to be minimized satisfies a weakerKurdyka-Lojiasewicz-type condition [Loj63, Kur98]. In particular, it makes itpossible to recover some pathological examples such as on-line learning forlogistic regression (see [Bac14]) and recursive quan- tile estimation (an evennon-convex situation).

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