A Proofs of the statistical analysis In the following proofs, we assume X to be Polish and Y = R

A.1 Upper bound for stochastic gradient descent This subsection is devoted to the proof of Theorem 1. Convergence of stochastic gradient descent for non-smooth problems is a known result. For completeness, we reproduce and adapt a usual proof to our setting. This corresponds to the gradient written in Algorithm 1. For resampling strategies, the proof is built on classical statistical learning theory considerations. Let us begin by controlling the estimation error.