Out-of-Distribution Generalization via Risk Extrapolation (REx)

David Krueger, Ethan Caballero, Joern-Henrik Jacobsen, Amy Zhang, Jonathan Binas, Rémi LE PRIOL, Dinghuai Zhang, Aaron Courville

Keywords: out of distribution, domain generalization, invariant risk minimization, robust optimization, invariant causal prediction, spurious features, generalization

Abstract: Distributional shift is one of the major obstacles when transferring machine learning prediction systems from the lab to the real world. To tackle this problem, we assume that variation across training domains is representative of the variation we might encounter at test time, but also that shifts at test time may be more extreme in magnitude. In particular, we show that reducing differences in risk across training domains can reduce a model’s sensitivity to a wide range of extreme distributional shifts, including the challenging setting where the input contains both causal and anti-causal elements. We motivate this approach, Risk Extrapolation (REx), as a form of robust optimization over a perturbation set of extrapolated domains (MM-REx), and propose a penalty on the variance of training risks (V-REx) as a simpler variant. We prove that variants of REx can recover the causal mechanisms of the targets, while also providing some robustness to changes in the input distribution (``covariate shift''). By appropriately trading-off robustness to causally induced distributional shifts and covariate shift, REx is able to outperform alternative methods such as Invariant Risk Minimization in situations where these types of shift co-occur.

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One-sentence Summary: Risk extrapolation is a simple robust optimization approache for Out-of-Distribution (OOD) generalization and invariant prediction.

Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/arxiv:2003.00688/code)

Reviewed Version (pdf): https://openreview.net/references/pdf?id=n0igWqZZgr