We study the problem of invariant learning when the environment labels are unknown. We focus on the invariant representation notion when the Bayes optimal conditional label distribution is the same across different environments. Previous work conducts Environment Inference (EI) by maximizing the penalty term from Invariant Risk Minimization (IRM) framework. The EI step uses a reference model which focuses on spurious correlations to efficiently reach a good environment partition. However, it is not clear how to find such a reference model. In this work, we propose to repeat the EI process and retrain an ERM model on the \textit{majority} environment inferred by the previous EI step. Under mild assumptions, we find that this iterative process helps learn a representation capturing the spurious correlation better than the single step. This results in better Environment Inference and better Invariant Learning. We show that this method outperforms baselines on both synthetic and real-world datasets.

本文研究了在环境标签未知的情况下的不变学习问题。我们提出了一种迭代的环境推断方法，结合环境内部的条件概率分布不变性，提高模型对冗余相关性的理解，从而实现更好的不变学习和环境推断表现。在合成和真实数据集上，实验证明了该方法的优越性。

循环环境推理用于不变性学习