Environment-Conditioned Tail Reweighting for Invariant Learning under Mixed Shifts

Out-of-distribution generalization becomes challenging when spurious correlations vary across environments while difficult or underrepresented samples remain insufficiently emphasized within them. Invariant learning and reweighting address complementary aspects of this mixed-shift problem, yet applying reweighting only to prediction leaves the invariance constraint evaluated on a different training risk. We introduce Environment-Conditioned Tail Reweighting (ECTR), which couples cross-environment TV invariance with within-environment adversarial tail weighting through a shared weighted risk. Sample weights are normalized within each environment, and the resulting risk is used consistently for both predictive learning and the total-variation (TV) stationarity penalty, while an environment-wise KL term controls adversarial concentration. Our analysis characterizes the stationarity-dependent weighting signal and its KL-regularized distributional interpretation, alongside conditional-risk and optimization properties under the stated assumptions. Controlled mixed-shift ablations consistently support the shared-risk coupling across three difficulty settings. Across synthetic and real-world benchmarks, ECTR achieves favorable results under both observed- and inferred-environment settings, including improvements over TV-based parent methods and strong performance against additional invariant-learning baselines. Training-corruption experiments further show that ECTR assigns less excess weight to corrupted samples than the tested fixed-tail rules. Together, these results provide a unified theoretical and empirical account of environment-conditioned tail reweighting for invariant learning under mixed shifts.