Domain generalization (DG) seeks predictors which perform well on unseen test distributions by leveraging data drawn from multiple related training distributions or domains. To achieve this, DG is commonly formulated as an average- or worst-case problem over the set of possible domains. However, predictors that perform well on average lack robustness while predictors that perform well in the worst case tend to be overly-conservative. To address this, we propose a new probabilistic framework for DG where the goal is to learn predictors that perform well with high probability. Our key idea is that distribution shifts seen during training should inform us of probable shifts at test time, which we realize by explicitly relating training and test domains as draws from the same underlying meta-distribution. To achieve probable DG, we propose a new optimization problem called Quantile Risk Minimization (QRM). By minimizing the $\alpha$-quantile of predictor's risk distribution over domains, QRM seeks predictors that perform well with probability $\alpha$. To solve QRM in practice, we propose the Empirical QRM (EQRM) algorithm and provide: (i) a generalization bound for EQRM; and (ii) the conditions under which EQRM recovers the causal predictor as $\alpha \to 1$. In our experiments, we introduce a more holistic quantile-focused evaluation protocol for DG and demonstrate that EQRM outperforms state-of-the-art baselines on datasets from WILDS and DomainBed.

翻译：域泛化旨在通过利用从多个相关训练分布或域中抽取的数据，构建能够在未见测试分布上表现良好的预测器。为此，域泛化通常被建模为对可能域集合的平均情形或最坏情形优化问题。然而，平均表现良好的预测器缺乏鲁棒性，而最坏情形表现良好的预测器则往往过于保守。为解决这一问题，我们提出了一种新的概率框架，其目标是学习能以高概率表现良好的预测器。我们的核心思想是，训练过程中观察到的分布偏移应能告知测试时可能出现的分布偏移，这通过将训练域和测试域明确关联为同一元分布中的样本实现。为实现可能的域泛化，我们提出一种称为分位数风险最小化的新优化问题。通过最小化预测器风险分布上的α分位数，QRM旨在学习能以概率α表现良好的预测器。为实际求解QRM，我们提出经验分位数风险最小化算法，并给出：（i）EQRM的泛化界；（ii）当α → 1时EQRM恢复因果预测器的条件。实验中，我们引入一种更全面的分位数量化评估协议，并证明EQRM在WILDS和DomainBed数据集上优于现有最佳基线方法。