Multi-domain generalization (mDG) is universally aimed to minimize the discrepancy between training and testing distributions to enhance marginal-to-label distribution mapping. However, existing mDG literature lacks a general learning objective paradigm and often imposes constraints on static target marginal distributions. In this paper, we propose to leverage a $Y$-mapping to relax the constraint. We rethink the learning objective for mDG and design a new \textbf{general learning objective} to interpret and analyze most existing mDG wisdom. This general objective is bifurcated into two synergistic amis: learning domain-independent conditional features and maximizing a posterior. Explorations also extend to two effective regularization terms that incorporate prior information and suppress invalid causality, alleviating the issues that come with relaxed constraints. We theoretically contribute an upper bound for the domain alignment of domain-independent conditional features, disclosing that many previous mDG endeavors actually \textbf{optimize partially the objective} and thus lead to limited performance. As such, our study distills a general learning objective into four practical components, providing a general, robust, and flexible mechanism to handle complex domain shifts. Extensive empirical results indicate that the proposed objective with $Y$-mapping leads to substantially better mDG performance in various downstream tasks, including regression, segmentation, and classification.

多领域泛化的研究旨在最小化训练和测试分布之间的差异，以增强边缘到标签分布映射，本论文提出利用Y映射来放松约束，重新思考多领域泛化的学习目标并设计了一个新的通用学习目标，揭示了之前的多领域泛化研究仅部分优化了目标导致了有限性能的问题，该研究提取出四个实际组成部分，提供了处理复杂领域转移的一种通用、强大和灵活的机制。

重新思考多领域泛化问题：通用学习目标