Selection of the Best Policy under Fairness Constraints for Subpopulations

Algorithmic decision-making in high-stakes settings can have profound impacts on individuals and populations. While much prior work studies fairness in static settings, recent results show that enforcing static fairness constraints may exacerbate long-run disparities. Motivated by this tension, we study a stylized sequential selection problem in which a decision-maker repeatedly selects individuals, affecting both immediate utility and the population distribution over time. We introduce notions of group fairness for both the short and long term and theoretically analyze the trade-off between fairness and utility via the Price of Fairness (PoF). We characterize optimal and fair policies in the short term and show that the PoF can be large even when group distributions are nearly identical. In contrast, we show that long-term disparities can vanish under simple investment policies that achieve a low PoF. We also empirically validate these theoretical observations using both synthetic and real datasets.

Algorithmic fairness methods are increasingly used to identify and mitigate bias in machine learning models, yet most approaches are evaluated in isolation and along single demographic axes. This limits practical guidance for selecting fairness strategies, where disparities may arise across intersectional subgroups and across multiple stages of the modeling lifecycle. This work presents FairSelect, a toolkit for systematically evaluating fairness mitigation strategies applied individually and in combination across preprocessing, inprocessing, and postprocessing stages. FairSelect supports multiple model architectures, intersectional subgroup evaluation, and comparison of fairness utility tradeoffs across baseline, single method, and multi level configurations. The framework was validated using synthetic clinical datasets designed to represent specific bias mechanisms and a real-world replication of two-year stroke risk prediction among patients with atrial fibrillation. Synthetic experiments showed that targeted fairness methods generally reduced intended subgroup disparities, while combined strategies produced larger average fairness improvements with modest utility tradeoffs. In the clinical prediction task, mitigation effects were highly variable, with some combinations improving both fairness and predictive performance while others were ineffective or counterproductive. These findings demonstrate that fairness interventions interact in nonadditive and context dependent ways. FairSelect provides a practical framework for systematically identifying fairness strategies that improve subgroup equity while preserving model performance in clinical machine learning.

In bandit problems, standard regret-minimizing algorithms treat exploration as an amortized cost, which can expose early participants to unfair ex-ante losses in settings such as clinical trials. Recent work addresses this by evaluating the sequence of per-round expected rewards through the generalized $p$-mean, interpolating between utilitarian welfare ($p=1$), Nash welfare ($p\to0$), and Rawlsian fairness ($p\to-\infty$). Although tight guarantees are known for $p\ge0$, the strictly fair regime $q=-p>0$ remains unresolved because negative-power means are dominated by the smallest per-round rewards. For $σ$-sub-Gaussian rewards with nonnegative means, the best prior algorithm relied on uniform early exploration and achieved regret $O(k^{(q+1)/2}/\sqrt{T})$, while the only general lower bound was the classical $Ω(σ\sqrt{k/T})$. Thus it was unclear whether the extra dependence on $k$ was intrinsic to strict fairness or an artifact of uniform exploration. We close this gap by identifying the exact polynomial price of strict fairness. Using a needle-in-haystack construction, we prove an algorithm-independent lower bound $Ω(σ\sqrt{k^{\max(1,q)}/T})$; for $q>1$, this shows that the penalty $k^{q/2}$ is information-theoretically unavoidable. We then introduce \textsf{UCB-HARE} (Harmonic Anchored Rank Exploration), which replaces uniform exploration with an inverse-weighted harmonic rank schedule protected by a certified positive-mean anchor. Its regret is $\widetilde{O}(σ\sqrt{k^{\max(1,q)}/T})$, matching the lower bound up to logarithmic factors. Experiments on synthetic instances confirm that \textsf{UCB-HARE} improves over uniform-exploration baselines, with gains increasing as $q$ grows.