Standard supervised learning breaks down under data distribution shift.\nHowever, the principle of independent causal mechanisms (ICM, Peters et al.\n(2017)) can turn this weakness into an opportunity: one can take advantage of\ndistribution shift between different environments during training in order to\nobtain more robust models. We propose a new gradient-based learning framework\nwhose objective function is derived from the ICM principle. We show\ntheoretically and experimentally that neural networks trained in this framework\nfocus on relations remaining invariant across environments and ignore unstable\nones. Moreover, we prove that the recovered stable relations correspond to the\ntrue causal mechanisms under certain conditions. In both regression and\nclassification, the resulting models generalize well to unseen scenarios where\ntraditionally trained models fail.\n