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...Journal of machine learning research submitted revised published implicit dierentiation for fast hyperparameter selection in non smooth convex quentin bertrand inria fr universite paris saclay cea palaiseau france klopfenstein u bourgogne institut mathematique de dijon mathurin massias gmail com malga dibris universita degli studi di genova italy mathieu blondel mblondel google brain team samuel vaiter math cnrs and alexandre gramfort joseph salmon umontpellier imag montpellier editor massimiliano pontil abstract finding the optimal hyperparameters a model can be cast as bilevel optimization problem typically solved using zero order techniques this work we study rst methods when inner is but show that forward mode proximal gradient descent coordinate yield sequences jacobians converging toward exact jacobian it possible to leverage smoothness speed up computation finally provide bound on error made hypergradient approximately results regression classication problems reveal computationa...