Fair Domain Generalization (FairDG)

• Fair Domain Generalization (FairDG) is a framework that learns from multiple source domains to achieve robust prediction and fairness on unseen target domains.
• It integrates invariant representation learning, causal fairness, and disentanglement to address both covariate and dependence shifts in data distributions.
• Key methodologies include conditional invariance, synthetic-domain generation, and multi-objective optimization to balance utility and fairness under domain shifts.

Fair Domain Generalization (FairDG) denotes the problem of learning from multiple labeled source domains so that a predictor remains both accurate and fair on an unseen target domain, without access to target-domain data during training. In the FairDG literature, a domain is typically modeled as a joint distribution over features, a sensitive attribute, and labels, and the central challenge is that both predictive structure and fairness constraints may change across environments. The field therefore combines domain generalization, invariant representation learning, causal fairness, disentanglement, synthetic-domain generation, and multi-objective optimization in order to study the transfer of both utility and fairness under shift (Pham et al., 2023, Zhao et al., 2023, Lin et al., 2023, Li et al., 2024, Jiang et al., 2024, Lian et al., 8 Jul 2025).

1. Definition and problem scope

The standard FairDG setting assumes multiple source domains and an unseen target domain. In one common formulation, source data come from multiple source domains $\mathcal{D}_{src}=\{\mathcal{D}^s\}_{s=1}^{S}$, where each domain is a joint distribution $\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$ over features $X$, sensitive attribute $Z$, and label $Y$. The goal is to learn from the source domains and then achieve both robust prediction and fairness in a target domain $\mathcal{D}_{tgt}$ whose distribution may differ from the training domains (Lin et al., 2024).

The literature distinguishes several types of shift. FEDORA states the two most prominent ones as covariate shift, $\mathbb{P}_X^s \neq \mathbb{P}_X^t$, and dependence shift, $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$ or $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$ (Zhao et al., 2023). FLAIR reformulates the second phenomenon as correlation shift between the sensitive attribute and the label, and emphasizes that existing methods usually address either covariate shift or correlation shift, but rarely both at the same time (Li et al., 2024). DCFDG studies a sequential setting in which domains arrive over time as $$\mathcal{S}=\{\mathcal{D}_1,\mathcal{D}_2,\dots,\mathcal{D}_T\}$$ and the target consists of unseen future domains $\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$0 (Lin et al., 2023).

Fairness is not fixed to a single criterion. Group-fairness formulations include Equalized Odds (EO) and Equal Opportunity (EP), expressed in FATDM as $\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$1 and $\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$2 (Pham et al., 2023). FADM evaluates Demographic Parity (DP) and Equalized Opportunity (EOp) through ratio metrics $\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$3 and $\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$4, where values closer to $\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$5 indicate better fairness (Lin et al., 2024). DCFDG adopts a counterfactual criterion,

$\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$6

for future domains (Lin et al., 2023). FLAIR reports both group fairness and individual fairness, using Demographic Parity difference $\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$7, $\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$8, and Consistency (Li et al., 2024). FAIRM emphasizes multi-calibration across environments (Li et al., 2024). This diversity of criteria reflects different operational notions of what it means for fairness to transfer.

2. Terminological background and historical development

The phrase fair generalization predates FairDG in a different sense. "Posing Fair Generalization Tasks for Natural Language Inference" defines fairness as whether a training dataset is sufficient for a baseline compositional learner to recover a target function $\mathbb{P}_{XZY} := \mathbb{P}(X,Z,Y)$9 exactly. There, a dataset $X$0 is fair with respect to $X$1 if it is sufficient for a baseline model that memorizes local input-output behavior at every internal node of a composition tree $X$2 to learn $X$3 perfectly (Geiger et al., 2019). That work studies compositional evaluation, not protected-group fairness under domain shift. This suggests two distinct uses of the word fair: one about whether an evaluation problem is underdetermined, the other about whether predictions behave equitably across sensitive groups.

Within the algorithmic-fairness literature, "Fairness and Accuracy under Domain Generalization" is presented as the first to study fairness transfer under domain generalization, asking whether a model trained to be fair and accurate on source domains remains fair and accurate on an unseen target domain (Pham et al., 2023). That paper makes fairness transfer itself the core object of study and derives sufficient conditions under which fairness and accuracy can be perfectly transferred via invariant representation learning.

A parallel precursor came from invariant representation learning. "Representation via Representations: Domain Generalization via Adversarially Learned Invariant Representations" explicitly states that it investigates censoring techniques first developed for learning fair representations and applies them to domain generalization by treating the domain label as the censored variable. The paper is best viewed as a FairDG-style method rather than a canonical fairness paper, because its primary objective is robust prediction on unseen domains rather than parity across protected groups (Deng et al., 2020). FAIRM later makes the bridge explicit by proposing a training environment-based oracle with both fairness and domain generalization properties under a diversity-type condition (Li et al., 2024).

3. Formal problem statements and evaluation criteria

Most FairDG formulations decompose the predictor into a representation map and a classifier. FATDM writes $X$4, with $X$5 and $X$6, and then studies how both expected loss and unfairness transfer from source domains $X$7 to an unseen target $X$8 (Pham et al., 2023). PAFDG formalizes FairDG as the simultaneous minimization of target-domain expected risk and target-domain fairness violation, where the target domain $X$9 is unseen during training and the fairness criterion is Equalized Odds (EOD) for multi-class classification and multi-group sensitive attributes (Lian et al., 8 Jul 2025).

The exact fairness metric depends on the paper. FATDM defines unfairness for binary classification and binary sensitive attributes by distances between group-conditional output distributions under Equalized Odds and Equal Opportunity (Pham et al., 2023). DCFDG reports Total Causal Effect (TCE) and Counterfactual Effect (CE), with smaller TCE and CE indicating better fairness (Lin et al., 2023). FEED reports Accuracy, $Z$0DP, $Z$1EOPP, and $Z$2EO, all fairness metrics being better when closer to zero (Jiang et al., 2024). DAID evaluates cross-domain deepfake detection by AUC and Skew, with lower Skew indicating fairer subgroup performance (Cheng et al., 3 Jul 2025). FLAIR adds Consistency and computes $Z$3-nearest neighbors within the same domain to adapt individual-fairness evaluation to domain generalization (Li et al., 2024).

Several papers make the unseen-target assumption explicit. DCFDG requires performance on future domains without requiring target data during training (Lin et al., 2023). FEDORA studies source domains $Z$4 and an unknown target domain $Z$5 that is inaccessible during training (Zhao et al., 2023). FLAIR states that training uses only finite source domains $Z$6, and test domains are inaccessible during training (Li et al., 2024). This assumption is central: FairDG is stricter than domain adaptation because it disallows target-domain access during learning.

4. Methodological families

The field is organized around a small number of recurring mechanisms: conditional invariance, disentanglement, synthetic-domain generation, causal adjustment, and explicit utility–fairness trade-off optimization.

Method family	Representative frameworks	Core mechanism
Conditional invariance	FATDM (Pham et al., 2023), FAIRM (Li et al., 2024)	Align $Z$7 or $Z$8; enforce invariant cross-moments and second moments
Disentanglement and transformation models	FEDORA (Zhao et al., 2023), DCFDG (Lin et al., 2023), FLAIR (Li et al., 2024), FEED (Jiang et al., 2024), FarconVAE (Oh et al., 2022)	Separate semantic/content information from style, environment, or sensitive factors
Generative fair data synthesis	FADM (Lin et al., 2024)	Generate fair synthetic data with label guidance and sensitive-information suppression
Causal fairness–generalization linkage	DAID (Cheng et al., 3 Jul 2025)	Back-door adjustment for data distribution and model capacity; fairness as intervention
Information-theoretic Pareto optimization	PAFDG (Lian et al., 8 Jul 2025)	Optimize utility and fairness jointly through conditional mutual information surrogates and Pareto fronts

FATDM operationalizes conditional invariance through a two-stage framework: first, label-conditional and label-and-sensitive-attribute-conditional density matching using translation models such as StarGAN or CycleGAN; second, invariant representation learning using translated samples and an MSE alignment term on a Gaussian representation $Z$9 (Pham et al., 2023). FAIRM instead formulates a training environment-based oracle that constrains cross-moments and second moments of the learned representation to be invariant across environments, and then derives an empirical version with finite-sample guarantees and a filter-then-optimize algorithm for high-dimensional linear models (Li et al., 2024).

Disentanglement-based methods dominate the current FairDG landscape. FEDORA assumes latent semantic, sensitive, and style factors; learns a transformation model $Y$0 with encoders $Y$1 and decoder $Y$2; then synthesizes new domains by sampling new sensitive and style factors while preserving the original class label (Zhao et al., 2023). DCFDG partitions latent factors into $Y$3, $Y$4, $Y$5, and $Y$6, uses LSTM priors for the environment variables, and trains the classifier using only semantic information (Lin et al., 2023). FLAIR separates content and style and then reconstructs fair content representations by clustering each sensitive subgroup into $Y$7 prototypes through a Gaussian mixture model, regularized so that prototype assignment probabilities match across sensitive groups (Li et al., 2024). FEED extends disentanglement to content, style, and sensitive vectors inside a MAML-style meta-learning loop, with synthetic-domain augmentation via a transformation $Y$8 (Jiang et al., 2024). FarconVAE is a VAE-style model with a non-sensitive latent $Y$9 and a sensitive latent $\mathcal{D}_{tgt}$0, trained with a distributional contrastive loss and a swap-reconstruction loss (Oh et al., 2022).

FADM approaches FairDG through data generation rather than direct debiasing. The method—called FADM: Fairness-Aware Diffusion with Meta-learning in the paper—pre-trains a score-based diffusion model $\mathcal{D}_{tgt}$1, a label classifier $\mathcal{D}_{tgt}$2, and a sensitive-attribute classifier $\mathcal{D}_{tgt}$3; then guides reverse-time diffusion both toward desired labels and toward high entropy in sensitive-attribute predictions, so that the generated synthetic data can be used by downstream classifiers under domain shift (Lin et al., 2024).

DAID and PAFDG make different theoretical moves. DAID frames fairness as a causal intervention $\mathcal{D}_{tgt}$4 and generalization performance as outcome $\mathcal{D}_{tgt}$5, controls the confounders $\mathcal{D}_{tgt}$6 and $\mathcal{D}_{tgt}$7, and implements this idea through Demographic-aware data rebalancing and Demographic-agnostic feature aggregation (Cheng et al., 3 Jul 2025). PAFDG derives mutual information upper bounds on both expected risk and EOD violation, then replaces the intractable conditional mutual information terms with conditional distance correlation and solves the resulting problem as a multi-objective optimization over the utility–fairness trade-off (Lian et al., 8 Jul 2025).

5. Empirical results and benchmark landscape

The empirical literature uses heterogeneous datasets, domains, and fairness metrics, so direct numerical comparison across papers is not meaningful. Even so, several representative results illustrate the scope of current FairDG evaluations.

Paper	Benchmark	Reported outcome
FADM (Lin et al., 2024)	Adult	Average ACC 84.97, Average $\mathcal{D}_{tgt}$8 0.91, Average $\mathcal{D}_{tgt}$9 0.75
DCFDG (Lin et al., 2023)	FairCircle / Adult / Chicago Crime	88.70 accuracy and 0.12 TCE; 69.85 accuracy and 0.22 TCE; 55.93 accuracy with TCE around $\mathbb{P}_X^s \neq \mathbb{P}_X^t$0
FLAIR (Li et al., 2024)	FairFace average	0.976 consistency / 0.007 $\mathbb{P}_X^s \neq \mathbb{P}_X^t$1 / 0.537 $\mathbb{P}_X^s \neq \mathbb{P}_X^t$2 / 97.10 accuracy
FEED (Jiang et al., 2024)	NYSF average	62.48 accuracy / 0.037 $\mathbb{P}_X^s \neq \mathbb{P}_X^t$3DP / 0.022 $\mathbb{P}_X^s \neq \mathbb{P}_X^t$4EOPP / 0.031 $\mathbb{P}_X^s \neq \mathbb{P}_X^t$5EO
DAID (Cheng et al., 3 Jul 2025)	DFDC / DFD / Celeb-DF	Skew $\mathbb{P}_X^s \neq \mathbb{P}_X^t$6, AUC $\mathbb{P}_X^s \neq \mathbb{P}_X^t$7; Skew $\mathbb{P}_X^s \neq \mathbb{P}_X^t$8, AUC $\mathbb{P}_X^s \neq \mathbb{P}_X^t$9; Skew $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$0, AUC $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$1
FarconVAE (Oh et al., 2022)	Waterbirds / cMNIST	Waterbirds: $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$2 acc 95.03, worst $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$3 acc 91.71, $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$4 acc 51.71; cMNIST: $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$5 acc 70.43, $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$6 acc 35.10

Several recurrent patterns emerge. First, methods that are fairness-aware but not designed for domain shift often degrade when the target distribution changes; FATDM was motivated precisely by the observation that a model fair during training may lead to an unexpected outcome during deployment (Pham et al., 2023). Second, methods that focus only on domain invariance can still retain substantial sensitive leakage; FarconVAE reports that IRM and Group-DRO improve label accuracy relative to ERM but still preserve strong sensitive predictability in learned representations, while its disentanglement step lowers $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$7-accuracy and improves worst-group performance (Oh et al., 2022). Third, complete FairDG pipelines often outperform either fairness-only or DG-only baselines on their native benchmarks. FLAIR is reported as consistently among the best in fairness and competitive in accuracy across RCMNIST, NYPD, and FairFace (Li et al., 2024). FEED reports the best average accuracy and strongest fairness on NYSF, and particularly strong fairness on YFCC100M-FDG (Jiang et al., 2024). PAFDG reports the best utility-fairness Pareto trade-off overall on CelebA, AffectNet, and Jigsaw (Lian et al., 8 Jul 2025).

A major theme concerns the status of the fairness–generalization trade-off. Many papers model the trade-off explicitly through penalty weights or Pareto optimization. FEED reports that on FairFace it slightly sacrifices accuracy relative to the best baseline but improves fairness meaningfully (Jiang et al., 2024). PAFDG turns the trade-off into an explicit Pareto-front problem (Lian et al., 8 Jul 2025). By contrast, DAID argues that the apparent trade-off can be partly spurious because fairness and generalization are both affected by shared confounders, and reports simultaneous improvement in both fairness and generalization after controlling them (Cheng et al., 3 Jul 2025). This suggests that the trade-off is problem-dependent rather than universally fixed.

6. Theory, assumptions, and open questions

The theoretical core of FairDG concerns what must be invariant for fairness to transfer. FATDM derives upper bounds on target expected loss and target unfairness, then shows that marginal invariance $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$8 is insufficient and can be harmful. The paper identifies the relevant conditions as label-conditional invariance $\mathbb{P}_{Y|Z}^s \neq \mathbb{P}_{Y|Z}^t$9 for accuracy transfer and label-and-sensitive-attribute-conditional invariance $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$0 for fairness transfer. It further proves that if the target domain is a mixture of source domains, then these conditional invariances are sufficient for perfect transfer (Pham et al., 2023). FAIRM provides a different theoretical route: under a diversity-type condition, its full-information oracle is minimax optimal for domain generalization over $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$1, and the empirical version is asymptotically multi-calibrated across environments (Li et al., 2024).

Later work broadens the theoretical toolkit. PAFDG derives mutual information-based upper bounds for target-domain risk and target-domain EOD violation, and simplifies the FairDG objective to maximizing $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$2 while minimizing $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$3 and $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$4 (Lian et al., 8 Jul 2025). DAID makes a causal claim: with fairness $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$5, generalization performance $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$6, and confounders $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$7 and $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$8, back-door adjustment yields a positive Average Causal Effect (ACE) of fairness on generalization, reported as an ACE gain = 2.35 percentage points with 95% CI $\mathbb{P}_{Z|Y}^s \neq \mathbb{P}_{Z|Y}^t$9 and two-sided $$\mathcal{S}=\{\mathcal{D}_1,\mathcal{D}_2,\dots,\mathcal{D}_T\}$$0 (Cheng et al., 3 Jul 2025). DCFDG extends counterfactual fairness to changing environments and ties it to a causal and variational representation-learning view (Lin et al., 2023).

These theories rely on strong structural assumptions. FLAIR assumes an underlying transformation model $$\mathcal{S}=\{\mathcal{D}_1,\mathcal{D}_2,\dots,\mathcal{D}_T\}$$1 and a content/style decomposition in which content is stable across domains and style is domain-specific; the paper explicitly notes that if domain shift cannot be captured by content/style separation, or if labels are not preserved under the assumed transformations, then the invariance argument becomes weaker (Li et al., 2024). FEED similarly depends on a generative transformation $$\mathcal{S}=\{\mathcal{D}_1,\mathcal{D}_2,\dots,\mathcal{D}_T\}$$2, binary sensitive attributes, and mainly binary classification experiments (Jiang et al., 2024). DCFDG assumes access to labeled sequential source domains and evaluates only classification (Lin et al., 2023). FADM assumes access to labeled source domains for meta-training and demonstrates the method on Adult in the provided excerpt (Lin et al., 2024). DAID requires demographic annotations and identifies extension to unlabeled fairness settings and richer multi-attribute fairness regimes as an important future direction (Cheng et al., 3 Jul 2025). PAFDG relies on source-domain and group labels during training and centers on group fairness via EO and EOD rather than broader fairness notions (Lian et al., 8 Jul 2025).

Taken together, these works suggest that FairDG is not a single algorithmic recipe but a family of responses to one question: what predictive information can be made stable across domains without preserving the sensitive dependencies that cause unfairness? Current answers range from density matching and invariant moments to causal disentanglement, diffusion-based data generation, and Pareto-optimal dependence minimization. The open issues identified in the literature include broader fairness definitions, weaker annotation assumptions, richer multi-group or intersectional settings, extension beyond classification, and more scalable training procedures under realistic domain heterogeneity (Pham et al., 2023, Li et al., 2024, Jiang et al., 2024, Lian et al., 8 Jul 2025).