Rethinking Multi-domain Generalization with A General Learning Objective
Zhaorui Tan Xi Yang Kaizhu Huang
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.