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Environment-Conditioned Tail Reweighting for Total Variation Invariant Risk Minimization

Wang Yuanchao, Lai Zhao-Rong, Zhong Tianqi, Li Fengnan

TL;DR

This work tackles out-of-distribution generalization under mixed distribution shifts, where both correlation shifts across environments and diversity shifts within environments degrade performance. It introduces Environment-Conditioned Tail Reweighting for Total Variation Invariant Risk Minimization (ECTR), a minimax framework that couples environment-conditioned tail reweighting with a TV-based IRM penalty, and extends to latent-environment inference when environment labels are unavailable. The core ideas are to compute environment-conditioned tail risks and enforce stationarity per environment, with an environment-wise KL regularizer to stabilize the tail adversary; a ZIN-style latent-environment inference variant enables training without explicit environment annotations. Empirically, ECTR yields consistent improvements across regression, tabular, time-series, and vision benchmarks, notably boosting worst-environment performance while maintaining strong average accuracy, demonstrating that tail robustness and TV-based invariance are complementary under mixed shifts. This approach provides a unified treatment that merges DRO-style tail robustness with invariant learning, offering practical robustness for real-world OOD scenarios where environment partitions are incomplete or noisy.

Abstract

Out-of-distribution (OOD) generalization remains challenging when models simultaneously encounter correlation shifts across environments and diversity shifts driven by rare or hard samples. Existing invariant risk minimization (IRM) methods primarily address spurious correlations at the environment level, but often overlook sample-level heterogeneity within environments, which can critically impact OOD performance. In this work, we propose \emph{Environment-Conditioned Tail Reweighting for Total Variation Invariant Risk Minimization} (ECTR), a unified framework that augments TV-based invariant learning with environment-conditioned tail reweighting to jointly address both types of distribution shift. By integrating environment-level invariance with within-environment robustness, the proposed approach makes these two mechanisms complementary under mixed distribution shifts. We further extend the framework to scenarios without explicit environment annotations by inferring latent environments through a minimax formulation. Experiments across regression, tabular, time-series, and image classification benchmarks under mixed distribution shifts demonstrate consistent improvements in both worst-environment and average OOD performance.

Environment-Conditioned Tail Reweighting for Total Variation Invariant Risk Minimization

TL;DR

This work tackles out-of-distribution generalization under mixed distribution shifts, where both correlation shifts across environments and diversity shifts within environments degrade performance. It introduces Environment-Conditioned Tail Reweighting for Total Variation Invariant Risk Minimization (ECTR), a minimax framework that couples environment-conditioned tail reweighting with a TV-based IRM penalty, and extends to latent-environment inference when environment labels are unavailable. The core ideas are to compute environment-conditioned tail risks and enforce stationarity per environment, with an environment-wise KL regularizer to stabilize the tail adversary; a ZIN-style latent-environment inference variant enables training without explicit environment annotations. Empirically, ECTR yields consistent improvements across regression, tabular, time-series, and vision benchmarks, notably boosting worst-environment performance while maintaining strong average accuracy, demonstrating that tail robustness and TV-based invariance are complementary under mixed shifts. This approach provides a unified treatment that merges DRO-style tail robustness with invariant learning, offering practical robustness for real-world OOD scenarios where environment partitions are incomplete or noisy.

Abstract

Out-of-distribution (OOD) generalization remains challenging when models simultaneously encounter correlation shifts across environments and diversity shifts driven by rare or hard samples. Existing invariant risk minimization (IRM) methods primarily address spurious correlations at the environment level, but often overlook sample-level heterogeneity within environments, which can critically impact OOD performance. In this work, we propose \emph{Environment-Conditioned Tail Reweighting for Total Variation Invariant Risk Minimization} (ECTR), a unified framework that augments TV-based invariant learning with environment-conditioned tail reweighting to jointly address both types of distribution shift. By integrating environment-level invariance with within-environment robustness, the proposed approach makes these two mechanisms complementary under mixed distribution shifts. We further extend the framework to scenarios without explicit environment annotations by inferring latent environments through a minimax formulation. Experiments across regression, tabular, time-series, and image classification benchmarks under mixed distribution shifts demonstrate consistent improvements in both worst-environment and average OOD performance.
Paper Structure (73 sections, 1 theorem, 31 equations, 1 figure, 2 tables, 1 algorithm)

This paper contains 73 sections, 1 theorem, 31 equations, 1 figure, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Tail reweighting
  3. Environment-conditioned
  4. Related Work
  5. Method categorization and our positioning.
  6. Shift taxonomy and benchmark regimes.
  7. Invariant learning and TV-based stationarity.
  8. Distributionally robust optimization, group robustness, and sample reweighting.
  9. Invariant learning with (and without) environment partitions.
  10. Preliminaries
  11. Multi-environment supervised learning (setup)
  12. ERM and TV-style invariant learning (TV-$\ell_1$ only)
  13. ECTR: environment-conditioned tail reweighting with stability regularization
  14. Environment membership.
  15. Environment-conditioned weights and tail risk.
  16. ...and 58 more sections

Key Result

Proposition 4.1

For fixed losses $\{\ell_i\}$ and $\beta>0$, the optimizer of Eq. eq:kl_reg_dro satisfies

Figures (1)

  • Figure 1: ECTR overview.

Theorems & Definitions (2)

  • Proposition 4.1: Gibbs form of the KL-regularized tail distribution
  • Remark 4.2: Interpolation between ERM and max-loss within each environment