Rethinking Multi-domain Generalization with A General Learning Objective

TL;DR

This work reframes multi-domain generalization around a general learning objective (GMDG) that relaxes the assumption of a static target distribution $P({\mathbf{Y}}|\mathcal{D})$ by introducing learnable mappings $\phi$ and $\psi$ that embed ${\mathbf{X}}$ and ${\mathbf{Y}}$ into a shared RKHS. The objective comprises four synergistic terms—learning domain-invariant representations (GAim1, GAim2) and maximizing posterior information (GReg1, GReg2)—plus two regularizers that integrate prior knowledge (GReg1) and suppress invalid causality (GReg2). The authors derive a generalized Jensen-Shannon Divergence (GJSD) based Alignment Upper Bound with Prior (PUB) to bound domain alignment and show how previous methods only partially optimized this objective. Empirically, GMDG improves performance across regression, segmentation, and classification on synthetic and standard benchmarks, often outperforming state-of-the-art methods with modest oracle usage. The results underscore the value of explicitly balancing invariant feature learning, prior information, and causality constraints for robust cross-domain generalization.

Abstract

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.

Figures (10)

• Figure 1: Segmentation and regression results of baselines and +GMDG on samples in unseen domains.
• Figure 2: (a) Diagram of causality in the proposed method. (b) Depth predictions on the unseen domain sample between model trained without and with GReg2.
• Figure 3: Toy experiments: Diagram of constructing the toy dataset.
• Figure 4: Toy experiments: Visualization of learned latent representations of different methods. Each color represents a domain.
• Figure 5: T-SNE map of latent features from classification models that were trained without and with GReg2.

Theorems & Definitions (3)

• Definition 1: GJSD
• Remark 1: Importance of ${\mathbf{Y}}$ mapping $\psi$
• Remark 2: Synergy of learning invariance, integrating prior knowledge and suppressing invalid causally