End-to-End Fairness Optimization with Fair Decision-Focused Learning
Authors: Yu Wang, Violet Xinying Chen
Organizations: School of Business Stevens Institute of Technology
Abstract
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.
Differentiable optimization layers are traditionally integrated in predict-then-optimize frameworks where a neural model estimates parameters that subsequently serve as fixed inputs to downstream decision-making optimization problems. In this work, we introduce the concept of a "fairness layer": a differentiable optimization layer appended to a model's output layer that guarantees a chosen notion of output parity is satisfied when integrated into a neural network. Additionally, we introduce an online primal-dual inference algorithm that provides provable aggregate fairness guarantees for streaming predictions with arbitrarily small batch sizes, where traditional per-batch constraints become overly restrictive. Numerical experiments demonstrate the effectiveness of the fairness layer and associated algorithm, and theoretical analysis characterizes the layer's differentiability and stability properties during model training and backpropagation. Our code for these experiments is publicly available on GitHub (https://github.com/dtroxell19/FairDL-ICML-2026.git) and our public Python package documentation can be found online: https://dtroxell19.github.io/fairness_training/.
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.
When sensitive attributes are continuous and high-dimensional − demographic score vectors, posteriors over attributes, age or income profiles − enforcing full statistical independence is often too restrictive, and existing relaxations rely on indirect dependence penalties or adversarial schemes that do not directly target the fairness-accuracy trade-off. We instead consider mean demographic parity through DPVar, the variance of the conditional-mean prediction given the sensitive attribute, and show that optimizing it yields a functional bilevel problem. We propose two algorithms for this problem: FBO, which uses a closed-form adjoint we derive for the squared-loss case to obtain an exact hypergradient, and ITD, which differentiates through unrolled inner steps and extends beyond squared loss. On synthetic data and a new semi-synthetic benchmark built from 60 tabular regression datasets, both methods achieve the lowest or near-lowest aggregate fairness-accuracy regret, and consistently match or outperform strong HSIC, adversarial, linear-dependence, and generalized-DP baselines.