DAFH: Fairness Without Demographic Labels

• DAFH is a fairness paradigm that improves outcomes for unobserved subpopulations by leveraging latent or surrogate group structures without relying on explicit sensitive attributes.
• It encompasses formulations like harmless Rawlsian fairness, preference-based fairness, and DRO, each setting specific no-harm conditions to prevent subgroup performance degradation.
• Optimization strategies range from loss-variance minimization to latent subgroup learning and active sampling, ensuring fairness gains without sacrificing overall predictive accuracy.

Demographic-Agnostic Fairness Without Harm (DAFH) denotes a family of machine-learning objectives and training procedures that seek to improve fairness across unknown, latent, or unobserved subpopulations without requiring protected attributes during training, while simultaneously avoiding degradation of overall utility or subgroup utility. In the recent literature, the term is not tied to a single formal criterion. Instead, it encompasses several closely related formulations: harmless Rawlsian fairness defined over every possible demographic partition, preference-based fairness with learned latent groups, distributionally robust worst-group control without observed demographics, and latent-subgroup or proxy-group methods that attempt to reduce disparity while preserving performance (Wang et al., 2024, Cai et al., 28 Sep 2025, Hashimoto et al., 2018, Hu et al., 2022).

1. Problem setting and motivation

DAFH arises from a recurring tension in algorithmic fairness. Group-fairness methods often presume access to sensitive attributes such as race, gender, or age, yet many practical settings do not provide them, or provide them incompletely, because of privacy, security, regulatory, or data-quality constraints. Several domains in the literature explicitly motivate this setting: chest-radiography databases with missing protected attributes, dermatological diagnosis where multiple sensitive attributes are naturally entangled in images, and repeated-deployment systems in which underrepresented groups may be harmed even when group labels are never observed (Queiroz et al., 2024, Chiu et al., 2024, Hashimoto et al., 2018).

The “without harm” clause is equally central. In some works it means that no subgroup should become worse off than under a baseline or previous iteration; in others it means that fairness gains should be obtained without increasing overall expected loss, or with only a limited decrease in aggregate accuracy. This distinction matters because DAFH is not merely fairness without demographics; it is fairness without demographics under an explicit non-maleficence or utility-preservation constraint. The resulting research program departs both from parity-only formulations, which may accept utility degradation, and from naive ERM, which can amplify disparity over time or bury minority losses inside population averages (Hashimoto et al., 2018, Wang et al., 2024).

A further motivation is intersectionality. When sensitive information is unavailable, incomplete, or too sparse to support multi-attribute auditing, latent or proxy subgroup discovery becomes attractive. Multiple works therefore replace visible demographics with appearance-based cohorts, gradient-defined soft groups, prototype-relative representations, or network-homophily structure, and then optimize fairness over those induced structures rather than over declared demographic labels (Luo et al., 2024, Liu et al., 2023, Masroor et al., 28 May 2026, Iskander et al., 2024).

2. Formal definitions of fairness and “no harm”

The DAFH literature contains multiple formalizations of both fairness and harm.

Formalization	Core condition	Representative source
Harmless Rawlsian fairness	minimize group-utility disparity for every possible grouping without increasing overall expected loss	(Wang et al., 2024)
Preference-based DAFH	rationality and envy-freeness under learned latent groups	(Cai et al., 28 Sep 2025)
Repeated-loss no-harm	no group’s risk increases across retraining iterations	(Hashimoto et al., 2018)
Active-sampling no-harm	new model has no lower accuracy risk and no higher disparity than the initial model	(Pang et al., 2024)
Ethical latent-subgroup no-harm	subgroup loss above a base model is penalized by a one-sided term	(Roy et al., 10 Mar 2026)

In harmless Rawlsian fairness, the objective is to reduce group-utility disparity for every possible demographic split even though no demographic prior is given. The key statement is that if group utility must be independent of every possible split $s$, then the per-example loss must be approximately independent of each example $z$, which in distributional terms forces the loss distribution toward a Dirac delta. This is formalized through the Maximum Utility Disparity,

$\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$

with the bound

$\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$

Thus variance collapse implies vanishing worst-case group disparity, but only if mean loss is simultaneously constrained so that the model does not degenerate into a uniformly bad predictor (Wang et al., 2024).

A different formalization appears in preference-based DAFH. Here a pooled classifier $h_0$ is compared against a learned group classifier $\theta:\mathcal X\to[K]$ and decoupled classifiers $h_1,\dots,h_K$. Fairness without harm consists of two conditions for every learned group $k$: rationality,

$R_k(h_k)\le R_k(h_0),$

and envy-freeness,

$R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$

This definition does not seek parity of outcomes; it seeks an allocation in which each latent group prefers its own classifier and is never worse off than under the pooled model (Cai et al., 28 Sep 2025).

An earlier demographic-agnostic notion of no-harm appears in repeated loss minimization. There the criterion is temporal: $z$0 The setting is dynamic deployment, where underrepresented groups may provide less feedback after receiving poorer predictions, causing ERM to amplify representation disparity across rounds. DAFH in this sense is satisfied if retraining never increases any subgroup’s risk, despite the subgroup identities remaining unobserved (Hashimoto et al., 2018).

Other works instantiate no-harm with respect to a baseline model. Influence-guided active sampling requires a new model $z$1 such that $z$2 and $z$3, whereas Flare introduces a one-sided penalty $z$4 so that subgroup loss increases relative to the base model are penalized during latent-cluster adaptation (Pang et al., 2024, Roy et al., 10 Mar 2026).

3. Core optimization paradigms

One major optimization route is loss-variance minimization under a utility constraint. VFair solves

$z$5

and in empirical form minimizes $z$6 subject to $z$7. The update combines gradients of mean loss and standard deviation,

$z$8

with

$z$9

This construction ensures descent on mean loss while reweighting higher-loss samples more heavily, thereby flattening the per-example loss profile without sacrificing the ERM optimum set (Wang et al., 2024).

A second route is DRO. In repeated loss minimization, the robust objective is

$\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$0

The intuition is that the adversary $\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$1 places more weight on high-loss examples, which may correspond to underrepresented groups. Under the assumption that each true group distribution lies inside the divergence ball, the DRO optimum controls the worst-group risk without group labels. In repeated retraining, the sequence of DRO objectives yields a monotonicity chain implying that the worst-group risk cannot increase over time (Hashimoto et al., 2018).

The same logic is specialized to survival analysis via a $\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$2-DRO ball with radius $\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$3, where $\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$4 is a lower bound on subgroup mass. The dual objective

$\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$5

implicitly up-weights high-loss patients and controls worst-case error over all latent subpopulations of mass at least $\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$6, again without observing demographics (Hu et al., 2022).

A third route learns the groups jointly with the predictors. In preference-based DAFH, the non-differentiable empirical objective is relaxed into a soft objective $\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$7 using soft group assignments $\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$8, surrogate losses $\ell_{\rm MUD}(\theta)=\max_k \E[\ell\mid s=k]-\min_k \E[\ell\mid s=k],$9, and a KL penalty $\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$0 encouraging balanced group sizes. Optimization proceeds by stochastic gradient ascent over the learned partition and the decoupled classifiers simultaneously (Cai et al., 28 Sep 2025).

A fourth route uses soft grouping through optimization geometry. The Graph of Gradients (GoG) constructs a KNN graph in last-layer gradient space, applies a one-layer GCN to produce normalized adversarial weights $\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$1, and solves the minimax problem

$\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$2

Theoretical results in that work argue that the gradient representation $\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$3 can carry more demographic signal than raw features alone, and the graph structure smooths weights over neighboring samples so that isolated noisy points do not dominate the adversary (Luo et al., 2024).

4. Latent groups, surrogate groups, and representation-level constructions

A substantial branch of DAFH replaces missing demographics with learned or induced group structure.

In medical imaging, one approach uses a foundation-model backbone as a frozen embedding extractor. Chest X-ray images are mapped to $\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$4, reduced with t-SNE, and clustered by DBSCAN into surrogate groups $\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$5. These groups can then be used for balanced re-sampling, fairness-aware regularization, or evaluation through $\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$6, $\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$7, and $\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$8. The method showed that cluster-balanced 30% sampling reduced the male-female representation gap from $\ell_{\rm MUD}(\theta)\le C\,\sqrt{\Var_z[\ell(z;\theta)]}.$9 to $h_0$0 on CheXpert and from $h_0$1 to $h_0$2 on NIH, but age was not separated nearly as cleanly by the embeddings (Queiroz et al., 2024).

A different imaging strategy is feature-space disentanglement rather than clustering. AttEN inserts blocks into a CNN that split features into $h_0$3 and $h_0$4, then minimizes a soft nearest-neighbor loss on disease-focused features while maximizing the same loss on skin-focused features. The total objective

$h_0$5

encourages disease information to be class-separable while making skin-related features uninformative for disease classification. Segment Anything Model masks are added to reinforce genuine diseased regions. On ISIC 2019, the ResNet-18 variant reduced $h_0$6 from $h_0$7 to $h_0$8 and $h_0$9 from $\theta:\mathcal X\to[K]$0 to $\theta:\mathcal X\to[K]$1, with $\theta:\mathcal X\to[K]$2 accuracy within $\theta:\mathcal X\to[K]$3–$\theta:\mathcal X\to[K]$4 percentage points (Chiu et al., 2024).

In language modeling, DAFair uses predefined or data-driven prototypical demographic texts rather than explicit labels. For each input embedding $\theta:\mathcal X\to[K]$5, similarities to paired prototypes are converted into a two-way softmax $\theta:\mathcal X\to[K]$6, and fairness is encouraged by minimizing

$\theta:\mathcal X\to[K]$7

The goal is to make each training example equally similar to each group prototype in representation space. On Bias-in-Bios with BERT, the method reduced TPR-GAP from $\theta:\mathcal X\to[K]$8 to $\theta:\mathcal X\to[K]$9 while maintaining $h_1,\dots,h_K$0 accuracy (Iskander et al., 2024).

Other works move further away from explicit groups. Group-free fairness on social networks defines a kernel-smoothed outcome vector $h_1,\dots,h_K$1 and measures between-“group” inequality as

$h_1,\dots,h_K$2

where $h_1,\dots,h_K$3 is a generalized-entropy index. The method never recovers group memberships; it uses homophily structure directly. In medical imaging, LHCF clusters image embeddings into hidden cohorts by GMM with BIC-selected $h_1,\dots,h_K$4, then optimizes either worst-cohort risk or cohort-gap loss. A stated lemma shows that if visible groups are unions of hidden cohorts, then any visible-group empirical risk is upper-bounded by the worst hidden-cohort risk (Liu et al., 2023, Masroor et al., 28 May 2026).

5. Empirical behavior across tasks and domains

The empirical record is heterogeneous, and one of the clearest patterns is that DAFH behaves differently in continuous-loss and quantized-loss regimes.

Under harmless Rawlsian fairness, regression tasks were reported to benefit substantially from variance minimization without utility loss. Across Law School, COMPAS, C&C Crime, AgeDB, and UCI Adult treated as an MSE proxy, VFair preserved Utility within $h_1,\dots,h_K$5–$h_1,\dots,h_K$6 of ERM $h_1,\dots,h_K$7 while cutting MUD by $h_1,\dots,h_K$8–$h_1,\dots,h_K$9, TUD by $k$0–$k$1, and VAR by $k$2–$k$3 absolute points in MSE. By contrast, classification gains on MUD and TUD were modest and often not statistically significant when fairness was assessed through accuracy, because accuracy is discrete; when a continuous “prediction error” metric was used instead, fairness gains reappeared (Wang et al., 2024).

DRO-based approaches have shown strong worst-group improvements in settings where worst-group risk is the primary concern. In repeated loss minimization, a reported example gave worst-group loss under ERM rising from $k$4 at round 1 to $k$5 at round 10, whereas DRO with $k$6 remained near-flat, from $k$7 to $k$8. In survival analysis, dro-cox reduced CI on FLC from $k$9 to $R_k(h_k)\le R_k(h_0),$0 with a c-index change from $R_k(h_k)\le R_k(h_0),$1 to $R_k(h_k)\le R_k(h_0),$2; on SEER it reduced CI from $R_k(h_k)\le R_k(h_0),$3 to $R_k(h_k)\le R_k(h_0),$4 with c-index moving from $R_k(h_k)\le R_k(h_0),$5 to $R_k(h_k)\le R_k(h_0),$6 (Hashimoto et al., 2018, Hu et al., 2022).

Latent-subgroup and soft-group methods also report measurable gains, though often with domain-specific trade-offs. GoG improved worst-subgroup accuracy and Equalized Odds on COMPAS, BNP, and MIMIC-III, with overall accuracy reductions of $R_k(h_k)\le R_k(h_0),$7, $R_k(h_k)\le R_k(h_0),$8, and $R_k(h_k)\le R_k(h_0),$9 absolute points respectively. Flare reported higher overall F1 than its baselines on OhioT1DM, EDA, and IHS, and positive $R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$0 on all three datasets, with fold-by-cluster plots showing $R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$1 for every cluster relative to the base model. LHCF reported that, for FairDi with a ResNet18 backbone, overall AUC increased from $R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$2 to $R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$3, min AUC from $R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$4 to $R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$5, and Gap AUC decreased from $R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$6 to $R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$7, despite never using demographic labels for training (Luo et al., 2024, Roy et al., 10 Mar 2026, Masroor et al., 28 May 2026).

Active data acquisition represents another empirical mode. Influence-Guided Active Sampling uses only a small validation set with group labels, scores unlabeled candidates by approximate fairness- and accuracy-influence, and selects points expected to improve fairness while retaining utility. Reported results on CelebA, UCI Adult, and COMPAS showed DP and EOp reductions of approximately $R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$8–$R_k(h_k)\le R_k(h_j),\quad \forall j\in[K].$9 relative to ERM and other active-learning baselines while maintaining or slightly improving accuracy, with less than $z$00 drop in the worst case (Pang et al., 2024).

6. Limitations, misconceptions, and open directions

A central limitation is that DAFH is not a single fairness doctrine. “Without harm” can mean no increase in subgroup risk across time, no loss relative to a pooled model, no reduction in global utility, or no degradation relative to a base model on learned latent clusters. Consequently, methods that all qualify as DAFH may optimize different quantities and may not be directly comparable (Hashimoto et al., 2018, Wang et al., 2024, Cai et al., 28 Sep 2025, Roy et al., 10 Mar 2026).

Another limitation is the quality of latent or surrogate subgroup discovery. Foundation-model embeddings may represent gender well but not age; DBSCAN may discard noise points and thereby exclude rare populations; appearance-based hidden cohorts can vary with clustering choice; and gradient graphs depend on the quality of learned representations and neighborhood construction. The literature therefore repeatedly notes purity, coverage, and interpretability issues for discovered groups (Queiroz et al., 2024, Luo et al., 2024, Masroor et al., 28 May 2026).

A common misconception is that DAFH eliminates the need for any demographic information anywhere in the pipeline. Several works remain demographic-agnostic only during training but still use demographic labels at validation or test time for auditing. Influence-guided active sampling requires a small validation set with sensitive attributes, and multiple medical-imaging papers evaluate fairness on known demographic slices even though those attributes are withheld during optimization (Pang et al., 2024, Chiu et al., 2024, Roy et al., 10 Mar 2026).

Another misconception is that reducing disparity is always equivalent to avoiding harm. Related work on positive-sum fairness argues that a larger disparity can be non-harmful if overall performance improves and no subgroup becomes worse off than under a baseline. That framework explicitly leverages sensitive attributes, so it is adjacent to DAFH rather than a DAFH method, but it clarifies why several DAFH papers insist on baseline-relative non-degradation rather than parity reduction alone (Belhadj et al., 2024).

Open directions recur across the literature: stronger guarantees on accuracy loss and subgroup stability; better latent-group discovery under noise, streaming, or non-IID data; extensions to regression, ranking, and unsupervised settings; adaptive selection of robustness radii, number of groups, or graph scales; and improved interpretability of learned subgroups. A plausible implication is that future DAFH systems will combine multiple signals—representation, loss, gradients, topology, and curvature—because the current literature shows each of these signals can reveal latent disadvantage that raw observed features alone may miss (Wang et al., 2024, Luo et al., 2024, Liu et al., 2023, Roy et al., 10 Mar 2026).