Learning Optimal Individualized Decision Rules with Conditional Demographic Parity

Demographic parity (DP) is a widely studied fairness criterion in regression, enforcing independence between the predictions and sensitive attributes. However, constraining the entire distribution can degrade predictive accuracy and may be unnecessary for many applications, where fairness concerns are localized to specific regions of the distribution. To overcome this issue, we propose a new framework for regression under DP that focuses on the tails of target distribution across sensitive groups. Our methodology builds on optimal transport theory. By enforcing fairness constraints only over targeted regions of the distribution, our approach enables more nuanced and context-sensitive interventions. Leveraging recent advances, we develop an interpretable and flexible algorithm that leverages the geometric structure of optimal transport. We provide theoretical guarantees, including risk bounds and fairness properties, and validate the method through experiments in regression settings.

Demographic parity (DP) is a widely used group fairness criterion requiring predictive distributions to be invariant across sensitive groups. While natural in classification, full distributional DP is often overly restrictive in regression and can lead to substantial accuracy loss. We propose a relaxation of DP tailored to regression, enforcing parity only at a finite set of quantile levels and/or score thresholds. Concretely, we introduce a novel (${\ell}$, Z)-fair predictor, which imposes groupwise CDF constraints of the form F f |S=s (z m ) = ${\ell}$ m for prescribed pairs (${\ell}$ m , z m ). For this setting, we derive closed-form characterizations of the optimal fair discretized predictor via a Lagrangian dual formulation and quantify the discretization cost, showing that the risk gap to the continuous optimum vanishes as the grid is refined. We further develop a model-agnostic post-processing algorithm based on two samples (labeled for learning a base regressor and unlabeled for calibration), and establish finite-sample guarantees on constraint violation and excess penalized risk. In addition, we introduce two alternative frameworks where we match group and marginal CDF values at selected score thresholds. In both settings, we provide closed-form solutions for the optimal fair discretized predictor. Experiments on synthetic and real datasets illustrate an interpretable fairness-accuracy trade-off, enabling targeted corrections at decision-relevant quantiles or thresholds while preserving predictive performance.

Designing fair algorithmic decision systems requires balancing model performance with fairness toward affected individuals: More fairness might require sacrificing some performance and vice versa, yet the space of possible trade-offs is still poorly understood. We investigate fairness in binary prediction-based decision problems by conceptualizing decision making as a multi-objective optimization problem that simultaneously considers decision-maker utility and group fairness. We investigate the set of Pareto-optimal decision rules for arbitrary utility functions for decision maker, arbitrary population distributions, and a wide range of group fairness metrics. We find that the Pareto frontier consists of deterministic, group-specific threshold rules applied to individuals' success probability. This complements existing optimality theorems from literature which, for specific fairness constraints, posit lower-bound threshold rules only. However we also show that, depending on the used fairness metric, the Pareto frontier may include upper-bound threshold rules, thus preferring individuals with lower success probabilities. We show that the location of the Pareto frontier depends only on population characteristics, utility functions and fairness score, but not on the technical design of the algorithm - our findings hold for pre-, in-, and post-processing approaches alike. Our results generalize existing optimality theorems for fairness-constrained classification and extend them to generalized fairness metrics and fairness principles, and to partial fairness regimes. This paper connects formal fairness research with legal and ethical requirements to search for less discriminatory alternatives, offering a principled foundation for evaluating and comparing algorithmic decision systems.