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Ensuring generalization to unseen environments remains a challenge. Domainshift can lead to substantially degraded performance unless shifts arewell-exercised within the available training environments. We introduce asimple robust estimation criterion -- transfer risk -- that is specificallygeared towards optimizing transfer to new environments. Effectively, thecriterion amounts to finding a representation that minimizes the risk ofapplying any optimal predictor trained on one environment to another. Thetransfer risk essentially decomposes into two terms, a direct transfer term anda weighted gradient-matching term arising from the optimality ofper-environment predictors. Although inspired by IRM, we show that transferrisk serves as a better out-of-distribution generalization criterion, boththeoretically and empirically. We further demonstrate the impact of optimizingsuch transfer risk on two controlled settings, each representing a differentpattern of environment shift, as well as on two real-world datasets.Experimentally, the approach outperforms baselines across variousout-of-distribution generalization tasks. Code is available at\url{https://github.com/Newbeeer/TRM}.

Learning Representations that Support Robust Transfer of Predictors