  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 condition [Loj63, Kur98]. In particular, it makes it
possible to recover some pathological examples such as on-line learning for
logistic regression (see [Bac14]) and recursive quan- tile estimation (an even
non-convex situation).
