Group Fairness

Omniprediction is a learning guarantee which requires a single predictor to be competitive relative to the best hypothesis from a benchmark class for any loss chosen from a family of loss functions. Loss Outcome Indistinguishability (loss OI for short) is a stronger notion that implies omniprediction. It requires the predicted distribution on labels to be indistinguishable from the true distribution to tests that depend on the loss functions and the benchmark class. Multiaccuracy and multicalibration are multigroup fairness notions that generalize classical notions of calibration and accuracy in expectation. Most known learning algorithms for omniprediction (both for the standard notion and for strengthenings like loss OI) rely on some version of these multigroup fairness notions, or on an intermediate notion called calibrated multiaccuracy. We ask if this is necessary: Does omniprediction require some form of multigroup fairness? We show that the answer is no for (plain) omniprediction, and yes for loss OI. First, a sequence of works shows that multicalibration or calibrated multiaccuracy imply omniprediction. We rule out even a weak converse, by showing that omniprediction for proper losses does not imply even accuracy in expectation, a much weaker notion than any of calibration, multiaccuracy, or multicalibration. Second, prior work showed how to achieve loss OI from a combination of calibration and multiaccuracy. We show a converse: loss OI is equivalent to a form of calibrated multiaccuracy.

Graph neural networks (GNNs) are the standard tool for node representation learning and are increasingly used in high-stakes settings. Their message-passing backbone, however, can amplify topological bias, raising fairness concerns. We study group fairness at the level of downstream predictions for node classification, link prediction, and node regression, and bound the demographic parity gap for an arbitrary number of sensitive groups. Our node classification bound is provably no looser than the closest prior result. For link prediction, ours is the first bound on the parity gap of the deployed sigmoid-activated prediction rather than a pre-activation proxy, and for node regression we provide the first such bound. Across all three tasks, the analysis identifies two distinct sources of bias: the separation between group means and the within-group covariance of the final representations. Building on this insight, we embed fairness into propagation itself by augmenting the convex smoothing problem underlying APPNP with a convex group-mean constraint and a within-group covariance regularizer. Unfolding projected gradient descent on this problem yields FairProp, whose layers pair a propagation step with a closed-form projection and which provably converges linearly to the unique fair optimum. Experiments on three tasks show that FairProp, even with exact group-mean equalization alone, provides a strong inductive bias that achieves excellent fairness-utility trade-offs against strong baselines.

Preference-based alignment methods such as reinforcement learning from human feedback (RLHF) and Nash learning from human feedback (NLHF) aggregate pairwise preferences to learn an LLM policy, but a natural goal is maximizing social welfare (average cardinal utility), which comparisons alone need not identify. Gölz, Haghtalab, and Yang (GHY) measure the gap by distortion: the worst-case ratio between the welfare of the best fixed lottery (distribution over responses) and of the learned lottery. They show NLHF is optimal when every user receives the same lottery. Account-based LLMs, however, have information about their users and can serve different lotteries to different people. We give an efficient algorithm, GLHF, that learns a single group-conditioned policy from one comparison per user. Under individual Bradley--Terry comparisons, GLHF asymptotically matches GHY's optimal population distortion bound simultaneously on every group in a prespecified, possibly overlapping collection, with sample complexity growing logarithmically in the number of groups and inversely with the smallest group mass. A sharper guarantee for groups with similar preferences approaches distortion of one when members share a feasible favorite response. In experiments using human coffee ratings and synthetic LLM-generated ratings, GLHF lowers distortion in every evaluated group and substantially reduces worst-group distortion relative to NLHF and other group-agnostic baselines.

As artificial intelligence is increasingly deployed, algorithmic unfairness has raised growing concerns and intensified demands for transparent fairness auditing. In practice, the tolerable degree of algorithmic unfairness depends on the specific legal, ethical, or application context. Given a prespecified tolerance threshold, an important statistical question is how to determine whether a group disparity exceeds the allowable tolerance across different auditing objectives. To address this problem, we develop a unified tolerance-based fairness auditing framework for two complementary auditing objectives: violation certification, which prioritizes control of false violation declarations, and sensitivity screening, which prioritizes reducing missed violations. For the first objective, we develop a constrained empirical likelihood test for formal settings that uses least-favorable-point calibration and can be combined with false flagging rate control for simultaneous subgroup auditing. For the second objective, we develop split empirical likelihood and adjusted split empirical likelihood tests using an adaptive boundary-proxy principle for early-warning settings. Numerical experiments show the distinct error-control--sensitivity trade-offs of these procedures. A COMPAS analysis illustrates the framework in predictive fairness auditing.

Over the past decade, Machine Learning (ML) has been trained under dual objectives: minimizing prediction error via Empirical Risk Minimization (ERM) while controlling unfairness bias. In practice, however, fairness-aware training often yields limited improvements over standard ERM, making reliable post hoc auditing essential. Existing auditing approaches for black-box models either rely on model reconstruction --exposing systems to extraction attacks-- or directly estimate fairness metrics, offering limited insight into which regions of the data distribution drive bias. More fundamentally, property-specific auditing --aimed at extracting only targeted fairness information without reconstructing the model-- remains poorly understood. In this work, we introduce the bias probe framework, which enables targeted and adaptive querying to reveal bias structure while preserving model confidentiality. Building on this framework, we propose ALeBi, an active auditor that learns such probes to efficiently estimate multi-group fairness metrics. We establish novel sample complexity guarantees governed by a property-specific complexity measure, resolving a previously posed open question, and extend our analysis to adversarial settings where the model owner may strategically obscure bias. Our results uncover a fundamental trade-off between model confidentiality and reliable auditing, and show that property-specific probing enables both accurate estimation and interpretable identification of high and low-bias regions. Extensive experiments support our theoretical findings and demonstrate the practical effectiveness of our approach.

Public institutions increasingly procure AI systems whose design they cannot inspect or change. In higher education, proprietary Early Warning Systems (EWS) leave colleges with few options beyond adjusting model outputs to address inequity. This raises the question of how fairness work is coordinated among vendors, institutions, advisors, and students with unequal power to change these systems? Using student records from a public college in Ontario, Canada, we evaluate six post-hoc fairness interventions on a research EWS under simulated procurement constraints. We compare fairness, accuracy, and demographic disparities, introducing error-type profiling to trace how interventions redistribute false positives and false negatives. Interventions redistributed disparities without consistently reducing them. Two implementations favored already-advantaged groups because they used group size to define disadvantage; small, marginalized groups remained poorly served. These findings show how procurement constraints and implementation choices shape the possibilities for fairness work. We call the resulting condition fairness theatre; dashboard metrics converge while groups' error burdens persist or worsen.

We view fairness as a property of distributional stability. Rather than assessing a predictor under a fixed data distribution, we study how its predictions change under perturbations that modify the composition of protected groups. A predictor is fair if it remains stable under such shifts. Under this perspective, several classical notions of fairness arise as stability with respect to specific perturbations, with the associated unfairness gap given by a Lipschitz constant of a prediction-rate functional. This formulation also yields guarantees that hold uniformly over a range of demographic compositions at test time, without requiring knowledge of the deployment distribution. It leads to a learning procedure based on convex combinations of reweighted predictors, formulated as a second-order cone program, for which we establish generalization bounds. Experiments on standard benchmarks illustrate the approach.

In this paper, a methodology to design fair graph convolutional neural networks (GCNs) is developed and tested over several application data sets. The graphs that are used as inputs to the network are constructed by a k-nearest neighbor-based preprocessing procedure, while fairness issues are considered in terms of the equalized odds criterion. To effectively incorporate the above heterogenous information, the equalized odds criterion is directly embedded into the model's optimization objective through an additional fairness-driven loss functional term. The proposed methodology investigates how varying the neighborhood size in the k-NN algorithm during graph construction influences both the classification performance and the fairness of the resulting models. Extensive experimentation is conducted on three real-world tabular datasets with known biases, evaluating the interplay between graph structure and fairness enforcement. The results demonstrate that the choice of the value of the parameter k critically impacts the performance trends, either steadily improving or peaking at intermediate values depending on dataset characteristics, while the application of fairness constraints significantly mitigates disparities in false positive and false negative rates across groups defined by the protected variable at hand, without incurring major sacrifices in overall accuracy. This study highlights the importance of jointly optimizing the graph construction process and fairness objectives in GCN-based learning, providing a systematic approach toward building more equitable and effective graph-based models.

Fairness audits in production ML typically occur once, at deployment, on a single domain. Both fail in practice: fairness can shift after retraining or a changing user base, and interventions validated on one dataset are rarely tested across the heterogeneous domains an organization deploys. We present FAPE (Fairness Auditing for Production Environments), a four-stage framework evaluating a single post-processing intervention, Fairlearn's ThresholdOptimizer, across eight domain evaluations: criminal justice, income prediction, legal admissions, credit lending, agricultural lending, a multi-domain benchmark corpus, healthcare, and education. Each is scored on demographic parity and equalized odds difference, plus disparate impact ratio and accuracy cost where computable. Intervention effectiveness tracks baseline disparity magnitude: across model-domain pairs the constraint improved disparity in 9 of 14 high-disparity cases and worsened it in 3 of 4 near-fair ones. Each of the five high-disparity exceptions reverses under one of two measurement checks, a minimum group size or thresholds fit on held-out data. A CUSUM monitor started at deployment, tested on a simulated shift, separates constrained models that never met a 0.1 parity convention from those that met it and later regressed. A single deployment-time audit is therefore an unreliable guide, which argues for baseline-disparity screening and continuous monitoring

Multi-view clustering (MVC) aims to uncover latent cluster structures by exploiting complementary information from multiple views. Despite substantial progress in clustering performance, fairness remains an important concern when MVC is applied to socially sensitive scenarios. Recent fair multi-view clustering methods have introduced fairness constraints into representation learning or clustering assignments. However, these methods generally treat different views under a largely uniform fairness mechanism, without explicitly distinguishing their varying levels of sensitive dependence during cross-view learning. In practice, different views may encode substantially different levels of sensitive information. Ignoring such cross-view discrepancy can allow highly sensitive-dependent views to influence less sensitive-dependent ones during cross-view learning, potentially degrading both clustering performance and fairness. To address this issue, we propose a novel multi-view fair clustering framework guided by cross-view sensitive information discrepancy. Specifically, we estimate the sensitive dependence of each view and develop a bias-ranked asymmetric alignment mechanism that encourages views with higher sensitive dependence to learn from those with lower sensitive dependence, while cross-view discrepancies are further exploited to adaptively regulate the alignment process. Moreover, fairness regularization is imposed on the consensus soft assignments to further promote group fairness. Extensive experiments on benchmark datasets demonstrate that the proposed method achieves a favorable balance between clustering quality and group fairness.

Principal Component Analysis (PCA) minimises aggregate reconstruction error, which can inadvertently represent majority subgroups with substantially higher fidelity than minority subgroups. Fairness-aware extensions of PCA correct this disparity but require group labels as input. We address the logically prior question: given only a data matrix, which binary partition of the data suffers the greatest representational disparity under a shared PCA projection? We formalise this as the max-disparity partition problem and propose a greedy local-search algorithm, grounded in the Fiduccia-Mattheyses bipartitioning framework, that discovers the disparity-maximising partition without any predefined group labels. Two benchmark algorithms, a fixed-projection sorting baseline and a simulated-annealing variant, confirm that the greedy solution is empirically near-optimal. Having identified the partition, we attribute the disparity to specific features via PCA loading scores and association rule mining, enabling a practitioner to assess whether the disadvantaged group corresponds to a human-meaningful minority. On the Predict Students' Dropout and Academic Success dataset, representational disparity is driven predominantly by institutional and programmatic proxies for socioeconomic disadvantage, with gender emerging as a secondary but consistent contributor within the disadvantaged group. The discovered partition is then passed directly to Fair PCA, completing a detect-explain-mitigate pipeline.

This paper presents the AR fairness metamodel, a framework designed to represent, analyze, and compare different fairness scenarios. The metamodel considers key elements, such as agents, resources, and their attributes, and enables the systematic definition and comparison of various fairness measures. We provide examples involving both discrete and continuous measures, including equality, equity, group fairness, individual fairness, the Gini index, the Theil index, Jain's fairness index, and a detailed fairness measure for Australia's Child Care Subsidy. We also explore relationships among group fairness, individual fairness, and envy-freeness, supported by formal proofs. At the conceptual modeling level, our approach builds on the Tiles framework, which offers modular components that can be connected to capture diverse fairness definitions. The goal is to make AR-based fairness definitions practical and adaptable across contexts, providing a clear way to define, compare, and evaluate them. An implementation of the Tiles framework is available as an open-source tool, and can support fairness modeling and evaluation across a wide range of applications.

The deployment of Federated Learning (FL) in multi-center clinical networks faces the challenge of "knowledge dominance," where high-volume hubs naturally overwhelm minority community nodes, implicitly treating the distinct clinical patterns of smaller cohorts as outliers. Existing geometric defenses provide a security baseline but leave this efficiency-fairness dilemma unresolved. To bridge this gap, we propose Fed-Equilibrium, a framework that advances the paradigm from simple defense to topological equilibrium. Unlike traditional aggregators, Fed-Equilibrium implements a sequential architectural synergy. It utilizes a two-stage gradient control cascade: Stage I (geometric quality assurance) enforces directional consistency via a cosine similarity funnel to filter malicious noise, creating a stabilized manifold; Stage II (topological Pareto control) then actively modulates verified contributions by identifying the optimal Pareto knee point. We validated this framework on a bi-national simulation integrating Canadian (CNODES) and U.S. (SyntheticMass) registries. Experimental results demonstrate that the system simultaneously secures the network against adversarial divergence while accommodating underrepresented signals. Notably, the minority U.S. spoke (representing less than 3% of data volume) achieved deep convergence comparable to the data-rich Canadian hub. This confirms that Fed-Equilibrium effectively counters "knowledge dominance," establishing a true "knowledge commons" where global generalizability does not come at the cost of local clinical representation.

Choosing when to retrain a deployed classifier requires assessing subgroup error rates across the sequence of models used, including periods between updates. We compare complete scheduled, loss-triggered, and subgroup-gap-triggered policies with retaining the initial model on the same observations and delayed labels. For true-positive and false-positive rates separately, the outcome is the paired difference in absolute subgroup gaps summed over deployment windows. Population evaluation in simulation, action records, and alternative schedules assess how measurement and retraining behaviour affect these comparisons. In a follow-up sample of 400 new trajectories per condition across two simulated drift regimes, all three policies had lower mean cumulative disparity, equivalent to reductions of 0.04 to 0.88 percentage points in the average gap per window. Evaluating the unchanged models against the known generating distributions preserved all mean directions, but finite-window and population comparisons agreed on whether updating increased, reduced or left cumulative disparity unchanged in 69 to 92 percent of trajectories. Under subgroup-specific drift, smaller true-positive-rate gaps accompanied lower sensitivity in both groups. In an exploratory American Community Survey replay, person weighting reversed all three race false-positive-rate mean comparisons without changing predictions or actions; all three weighted intervals included zero. Policy comparisons require group-specific rates, action distributions, and an explicit evaluation population alongside mean disparity. These analyses are non-confirmatory. Shared replay requires policy-independent observations and complete labels after the specified delay.

Fairness in clustering has attracted sustained research interest, motivated by the need to ensure equitable representation of protected groups in machine learning applications. We study fair $k$-means clustering in Euclidean space, where the proportion of each protected group in every cluster must lie within specified lower and upper bounds. These constraints make it challenging to determine both cluster centers and point assignments. We propose an approximation algorithm that combines a linear programming relaxation with geometric transformations of the input to construct candidate center sets. Given a $ρ$-approximate algorithm for weighted $k$-means and any $ε>0$, our algorithm returns a fractional solution whose cost is at most $1+(3-1/Γ)ρ+O(ε)$ times the optimal integral fair cost, where $Γ\approx6.357$ is an upper bound on the integrality gap of the standard Euclidean $k$-means LP. With a PTAS as the subroutine, the approximation ratio becomes $3.8427+O(ε)$, improving the previous factor of $5+O(ε)$ to below $4$. The solution satisfies all fairness constraints exactly and can be rounded to an integral assignment with a bounded additive violation of fairness and no increase in cost. The same approximation guarantee extends to the $k$-sparse Wasserstein barycenter problem.

Shortcut learning denotes the widespread situation in which a classifier exploits spurious correlations rather than diagnostic features. Existing mitigation strategies mostly aim to learn shortcut-invariant representations; their empirical success is limited and they cannot be applied to classifiers using frozen foundation model encoders. We propose to reframe shortcut learning as fundamentally a calibration problem: unconstrained learning implicitly calibrates each shortcut group to its training set disease prevalence, rendering the resulting classifier necessarily over-confident in one group and under-confident in the other. Building on this insight, we prevalence-equalize calibration between shortcut groups through two encoder-agnostic methods, an in-processing regularizer and a post-hoc prevalence-equalized recalibration step. Across chest-drain-pneumothorax benchmarks on CheXpert and SIIM-ACR, spanning fine-tuned CNNs and frozen foundation-model backbones, both methods substantially outperform all baselines. Post-hoc recalibration of a standard ERM-trained DenseNet raises misaligned-group AUROC from 0.23 to 0.73, indicating that shortcut reliance degrades the classification head rather than the underlying representation. Besides two new state-of-the-art shortcut mitigation approaches, our findings more fundamentally connect shortcut learning to calibration theory and algorithmic fairness.

Face recognition systems have been shown to be biased toward certain demographic groups by exhibiting different error rates across gender, age, or ethnicity. Though the imbalance of the training data with respect to these demographics is one cause of this bias, training on artificially balanced groups does not completely mitigate the problem. For deployment, face recognition typically works at operating points allowing very low false match rates and, hence, on the tail of the non-match score distribution. While class balancing can improve the means of these distributions, the aim of our approach is to improve fairness by addressing the behavior in the tail. Particularly, we propose the Demographic-based Supervised Contrastive loss (DeSCon) for face recognition, which relies on a well-designed composition of training batches and demographic-aware pair selection. Our experimental evaluation on both demographically-labeled datasets and standard verification benchmarks shows that DeSCon can improve fairness beyond balancing training datasets while maintaining competitive verification performance. Source code is available upon request.

Group alignment adapts a language model to a demographic group to produce responses that reflect the group's opinions, values, and preferences. Sycophancy, a well-documented by-product of alignment, causes the model to over-agree with the user regardless of factual and objective information. However, existing group alignment methods and evaluations focus only on how closely the model matches the group's opinions, overlooking the induced change in sycophantic behaviour. To bridge this gap, we introduce \textbf{G}roup \textbf{A}lignment-induced \textbf{S}ycophancy (GAS) and systematically evaluate alignment across 3 methods, 4 models and 13 demographic groups, on both the intended gain in opinion alignment and the unintended shift in sycophancy. We find that gain and shift are non-uniform across groups: under an identical budget, some groups receive larger gains in opinion alignment than others, and the induced sycophancy shift forms a group-specific profile rather than a single-dimensional change. These results suggest that group alignment should be reported as a two-sided, multi-dimensional profile rather than a single fit score that accounts for per-group differences when adapting LLMs to diverse populations.

Reinforcement Learning from Human Feedback (RLHF) aggregates heterogeneous preferences into a single reward model, assuming preference homogeneity. When preferences are heterogeneous, this aggregation induces a procedural fairness failure where majority preference groups dominate reward learning while minority preferences are systematically under-represented. This work defines procedural fairness in alignment as preserving distinct preference signals during reward modeling and shows that standard RLHF violates this via preference averaging. Preference-Aware RLHF (PA-RLHF) is introduced, separating optimization across preference modes at the reward learning stage. In a controlled setting, PA-RLHF improves overall alignment accuracy from 46.9% to 67.9% and reduces the fairness gap between best and worst aligned groups from 15.9 to 9.6 percentage points. These results show that procedural fairness failures in alignment can arise from structural design choices in reward learning, even in controlled, noise-free settings, with direct implications for large language models and agentic systems, where biased reward models can compound inequities across sequential decisions.

In fair ranked link prediction, demographic parity ($Δ_\mathrm{DP}$) is a common fairness metric. Yet, Mattos et al. (2025) argue that it fails to detect exposure bias because it ignores where links appear in the ranking. In this study, we reproduce this claim by showing that $Δ_\mathrm{DP}$ can indicate aggregate parity even when some subgroup-pair links are systematically ranked lower than others. The proposed rank-aware Normalized Discounted KL-divergence (NDKL), however, does detect such disparities. We also reproduce the effectiveness of MORAL, a post-processing method that improves exposure-based fairness while maintaining competitive utility. Beyond reproduction, we assess robustness using synthetic homophily settings, categorical sensitive attributes, and additional fairness and utility metrics, including subgroup-pair-adapted Attention-Weighted Rank Fairness (AWRF). Overall, our results show that exposure-based metrics uncover biases hidden by $Δ_\mathrm{DP}$ and that MORAL reduces these biases with minimal utility loss across diverse settings and datasets. We release a corrected, reproducible implementation at https://github.com/Floris93100/reproducing-MORAL.

Allocating public-school investment effectively and fairly is difficult when school access depends on residence. School improvements can raise nearby housing demand and prices, reshape enrollment, and potentially limit access for lower-income households. These effects evolve as residential sorting changes school composition, quality, and future investment needs. Existing approaches often study school funding, household choice, and housing markets separately, while static models can miss their interconnected, long-term effects. We address this gap with a dynamic multi-agent framework that links government investment, household sorting, housing prices, population turnover, enrollment, and evolving school quality. A government planner uses reinforcement learning (RL) to identify multiyear allocation policies that account for household responses while balancing aggregate educational access and equity. In simulations, our RL-based policy attains the highest access level (0.4780) and second-lowest access Gini coefficient (0.0164) among representative baselines, demonstrating a favorable effectiveness-equity balance. The results also indicate reduced socioeconomic stratification in educational access. By making education-housing feedback explicit, our framework supports long-term analysis of how school investment shapes educational opportunity over time.

Collaborative machine learning among financial institutions must be both group-fair and robust against deliberate adversarial manipulation. Existing fairness-aware aggregation methods remain formally vulnerable to fairness poisoning: a malicious client maximizing group disparity while preserving accuracy evades accuracy-based Byzantine defenses, and in our threat model FairFed's gap-based weighting can be gamed by an adversary who observes the global fairness score. We present Fairis, a server-side reweighting scheme in which each client's update receives the normalized weight $ω_k = \bar{w}_k / \sum_j \bar{w}_j$ built from the unnormalized score $\bar{w}_k = η- \mathcal{F}_k$, with $\mathcal{F}_k \in [0,1]$ the local Equal Opportunity Difference and $η> 1$ a security parameter. We prove three properties, Monotone Weight Reduction (MWR), Demographic Participation, and Non-Gamesmanship, extend MWR to colluding minority coalitions, and show that combining MWR with server-side norm clipping bounds the adversary's displacement of the global model by $ω_0 C$, strictly decreasing in its own reported disparity. Assuming honest score reporting, an assumption this paper does not discharge, Fairis is the only rule evaluated that guarantees every client strictly positive weight while provably reducing an adversary's weight monotonically in its bias; clipped FairFed can reach a lower weight but guarantees nothing and zeroes a client outright on Taiwan Credit. Against an adversary stealthy enough to evade accuracy-based defenses, within 0.04 accuracy of benign, Fairis cuts its weight by 41 to 54% below a size-blind control on Taiwan. On routine non-IID partitions no rule dominates, and a uniform-weighting ablation shows that containment tracks how far the adversary's score separates from the honest mean, providing none when the honest population is already unfair.

Fairness in AI systems has become more important with recent regulatory demands, such as the EU AI Act. Traditional approaches often do not take into account philosophical ethics and social awareness. Variable selection processes, in particular, can introduce implicit bias, affecting equity across different subgroups. We discuss a mathematical approach that evaluates fairness in AI, aligning mathematical methodologies with ethical considerations and regulatory requirements. Our aim is to advocate for interdisciplinary collaboration to address fairness, emphasizing the importance of understanding broader ethical and societal contexts. Our approach emphasizes maintaining all potentially relevant variables to allow for more granular fairness assessments and to reduce implicit bias. The findings suggest that the exclusion of sensitive or critical variables may compromise equity between subgroups. In contrast, retaining all relevant variables could reduce implicit bias. Thus, the interdisciplinary approach could provide deeper insight into the ethical implications and compliance with regulatory standards. By integrating a mathematical approach with ethical and social awareness, we suggest more equitable outcomes and responsible AI deployment. This work underscores the necessity of interdisciplinary collaboration in effectively addressing fairness in AI systems aligned with the objectives of the European Union's AI Act, which seeks to promote trustworthy and fair AI systems.

Fairness audits are increasingly mandated in high-stakes applications such as hiring, lending, and automated decision-making. Recent work has established fundamental impossibility results for black-box fairness auditing, showing that sufficiently expressive models can evade any auditing strategy. We complement these results by quantifying the extent of unavoidable post-audit manipulation under finite audit resources. We formulate fairness auditing as a min-max optimization between a computationally unbounded company and a budget-constrained auditor. We study two auditing regimes: (i) a budgeted auditor that certifies fairness using a fixed-size audit set, and (ii) a budgeted α-tolerant auditor that additionally requires the audit set to estimate the fairness of the certified model within an α approximation. For both settings, we derive explicit lower bounds on the worst-case post-audit demographic parity deviation as functions of the audit budget, group imbalance, and fairness tolerance. Finally, we empirically illustrate these theoretical limits using simple audit-set construction heuristics with linear and neural network classifiers. Our results demonstrate that increasing audit resources reduces, but does not eliminate, the scope for post-audit manipulation, highlighting fundamental limitations of finite-budget fairness certification.

Many real-world systems rely on predictive models to inform decisions, and fairness concerns arise in both the prediction and decision stages. We introduce end-to-end fairness optimization (E2EFO) as a unifying framework that integrates fairness across the prediction-to-decision pipeline. We focus on resource allocation with group-based fairness: the prediction task estimates allocation impacts while limiting accuracy disparity across groups, and the decision task distributes those impacts equitably by optimizing a group-based alpha-fairness measure. Within this framework, we propose fair decision-focused learning (FDFL), a training paradigm that jointly accounts for prediction accuracy, prediction fairness, and decision regret -- the loss in decision fairness due to imperfect predictions. FDFL trains the predictor by gradient descent, combining the objective gradients through multi-task learning techniques. The core computational challenge is the decision Jacobian with respect to the predictor parameters: we derive exact closed-form formulas for a tractable class of fair allocation and apply a differentiable optimization layer in the general case. We further establish a finite-sample generalization bound for the scalarized FDFL objective. Numerical experiments on a healthcare-based single resource allocation and a synthetic multiple resource allocation illustrate the value of jointly accounting for prediction fairness and decision fairness in prediction-informed decision-making.

Resource allocation across multiple agent groups arises in many applications including e-commerce recommendation systems, housing assignment, and course allocation, and is commonly formulated as an optimization problem with diversity constraints to ensure group fairness. Existing approaches typically enforce these constraints as hard conditions, which overly restrict the feasible solution space and often lead to suboptimal allocations. In this paper, we propose PRA, a parameterized framework for fair resource allocation under diversity constraints. Inspired by the use of risk-aversion parameters in economic models, PRA introduces a set of controllable inequality-aversion parameters to softly regulate group-level diversity, thereby enabling flexible trade-offs between fairness and allocation efficiency. With appropriately calibrated parameters, PRA yields fairness-optimal assignments that comply with the specified diversity constraints. To accommodate additional application-specific constraints, we further extend the framework to an adaptive variant, APRA. We establish that the optimality of both PRA and APRA holds regardless of the chosen fairness metric and the nature of the additional constraints, underscoring the generality and robustness of our approach. Extensive experiments on three real-world applications demonstrate that our proposed framework consistently outperforms existing baselines in both effectiveness and robustness.

We study a restless multi-armed bandit (RMAB) problem for a stochastic deadline scheduling application. RMAB problems are solved using the Whittle index policy. The goal in RMAB is to maximize the expected cumulative discounted reward maximization. The Whittle index policy maximizes reward, but is not fair among two classes. In this paper, we introduce fairness criteria and study an outcome-fair model for RMAB which allows fairness for jobs and users structurally disadvantaged demographic classes. We formulate an outcome fair stochastic deadline scheduling problem as RMAB, and we develop the outcome fair Whittle index policy. We define a virtual queue mechanism that dynamically enforces long-term completion rate guaranties across demographic groups. We analyze a standard Whittle index policy and the outcome-fair index policy. We demonstrate the performance of our algorithms with numerical examples. We compare policies---Whittle index policy (no fairness), input-fairness Whittle index policy, outcome fair Whittle index policy. We observe that the outcome-fair Whittle index policy provides better fairness among classes compared to other policies. We demonstrate a trade off between fairness and profit. This decreases as the server capacity increases.

Minimum-exposure constraints arise in recommendation, content curation, and regulated allocation when each provider, arm, or group must receive guaranteed exposure inside a period rather than only in aggregate. We study stochastic bandits with exact exposure floors and show that the right object is a rounding problem: a fractional fair schedule is realized as integral pulls, and the exposure error is exactly a discrepancy vector. The main contribution is a blockwise model with time-varying floors. BDQ-UCB satisfies every block floor deterministically and has fair regret governed by the nonmandatory budget $R$, not the horizon $T$, with high-probability regret $O(\sqrt{KR\log(KT)})$. A MOSS residual variant attains $O(\sqrt{KR})$, and a matching lower bound gives the minimax rate $Θ(\sqrt{KR})$, even with positive mandatory exposure; a kl-UCB$^{++}$ residual rule adds instance-dependent optimality. The formulation becomes essential for overlapping group floors: per-arm rounding can violate a group constraint by $Ω(s)$ in the group size, whereas Beck--Fiala null-space rounding meets every group floor within the block budget with violation below the arm degree $t$, and composes with UCB at the same $R$-parametrized regret. For learned group plans, we close disjoint systems at $\widetildeΘ(\sqrt{KT})$, give a dual-ledger decomposition explaining why naive index rules fail under overlap, and prove a plan-sampling rule that is pathwise feasible under an initial cover-slack condition and attains a conditional $\widetilde O(\sqrt{KT})$ guarantee, leaving the condition-free overlap rate open. Experiments on synthetic floors, MovieLens-100k genre exposure, and deployment stress tests show exact feasibility without penalty tuning and regret competitive with tuned Lagrangian baselines.

Fair clustering aims to make cluster assignments independent of sensitive attributes, but this goal becomes challenging when multiple sensitive attributes jointly define many subgroups. In such settings, directly extending existing fair clustering algorithms is computationally expensive or numerically unstable, especially when the number of subgroups grows exponentially and some subgroups contain only a few instances. To address these challenges, we define a subgroup-fairness gap for clustering and derive a covariance-based surrogate that exactly matches this gap. We then introduce a continuous relaxation of the surrogate, enabling efficient gradient-based optimization and yielding our proposed algorithm, COVA-FC. We also show that subgroup fairness alone does not imply marginal fairness, and extend our framework to capture a subgroup-marginal-fairness gap. Experiments on benchmark datasets show that COVA-FC achieves competitive cost-fairness trade-offs and improves computational efficiency over existing baselines in both subgroup and higher-order marginal settings.

The problem of fair multi-agent coordination in decentralized settings is one of the most pressing challenges for building efficient collaborative systems. Resource allocation is based on optimized collective arrangements accounting for agents' needs. Such coordination should not only be computationally efficient but also account for fairness, i.e., equitable redistribution of costs incurred by all agents. Recent literature has proposed several algorithms that efficiently determine optimal plan combinations balancing system-wide efficiency and individual discomfort of agents in a centralized setting. However, these works do not address equitable resource optimization in fully decentralized scenarios, specifically, the optimized redistribution of discomfort among coordinating agents so that none experiences a discomfort level that could lead to loss of incentive or polarization that can disrupt planned operations. In this work, we study the problem of optimizing three objectives: (i) system-wide efficiency, (ii) individuals' comfort and (iii) fairness (i.e., balancing of incurred discomfort costs) in decentralized multi-agent coordination. We design a novel model to optimize those three orthogonal objectives, without any substantial increase in communication and computational overhead. Through experiments on two real-world datasets, we validate the model and demonstrate that it can achieve fairer optimization outcomes, while satisfying agents' preferences and system goals.