Robustness methods estimate the task covariance Sigma_task, and the matching principle requires penalty matrices to have range covering that of Sigma_task to zero deployment drift.
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Invariant Risk Minimization
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We introduce Invariant Risk Minimization (IRM), a learning paradigm to estimate invariant correlations across multiple training distributions. To achieve this goal, IRM learns a data representation such that the optimal classifier, on top of that data representation, matches for all training distributions. Through theory and experiments, we show how the invariances learned by IRM relate to the causal structures governing the data and enable out-of-distribution generalization.
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- abstract We introduce Invariant Risk Minimization (IRM), a learning paradigm to estimate invariant correlations across multiple training distributions. To achieve this goal, IRM learns a data representation such that the optimal classifier, on top of that data representation, matches for all training distributions. Through theory and experiments, we show how the invariances learned by IRM relate to the causal structures governing the data and enable out-of-distribution generalization.
- background Θ ⊆ Rd are convex and compact, and letθ∗ ∈ Θ be a minimizer of the worst-group objectiveR(θ). Then there exists a distributionQ∗ ∈ Q such thatθ∗ ∈ arg minθ Ez∼Q∗[ℓ(θ;z)]. However, this equivalence breaks down when the lossℓ is non-convex: Counterexample 1. Consider a uniform data distributionP supported on two points Z = {z1,z 2}, and letℓ(θ;z) be as in Figure 4, withΘ = [0, 1]. The DRO solutionθ∗ achieves a worst-case loss of R(θ∗) = 0.6. Now consider any weights (w1,w 2) ∈ ∆2 and w.l.o.g. letw
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