Fairness Uncertainty Quantification: A Constrained Stochastic Optimization Perspective

Abhishek Roy, Prasant Mohapatra
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:5845-5865, 2026.

Abstract

In this paper, we construct confidence interval (CI) for the test-unfairness of a group-fairness aware classifier trained by Stochastic Gradient Descent ({SGD}) type algorithms. Since these algorithms are almost invariably used to train modern machine learning models, the learned parameters—and consequently their fairness—are inherently random. We quantify this randomness, which can have far-reaching consequences, especially for sensitive applications. Viewing fairness-aware classification through the lens of constrained optimization allows us to leverage tools from stochastic approximation theory to establish the asymptotic normality of the estimated parameters. Existing work typically provides fairness guarantees either in expectation or for the exact minimizer of the constrained objective \citep{del2020review, celis2019classification}, without accounting for the stochasticity induced by the optimization algorithm itself. To construct CIs for fairness in practice, we develop an easily parallelizable online multiplier bootstrap procedure. In doing so, we also extend theoretical guarantees for online bootstrap methods from unconstrained {SGD} to the constrained optimization setting which may be of independent interest. We illustrate the effectiveness of our approach through extensive simulations and experiments on benchmark datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-roy26b, title = {Fairness Uncertainty Quantification: A Constrained Stochastic Optimization Perspective}, author = {Roy, Abhishek and Mohapatra, Prasant}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {5845--5865}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/roy26b/roy26b.pdf}, url = {https://proceedings.mlr.press/v337/roy26b.html}, abstract = {In this paper, we construct confidence interval (CI) for the test-unfairness of a group-fairness aware classifier trained by Stochastic Gradient Descent ({SGD}) type algorithms. Since these algorithms are almost invariably used to train modern machine learning models, the learned parameters—and consequently their fairness—are inherently random. We quantify this randomness, which can have far-reaching consequences, especially for sensitive applications. Viewing fairness-aware classification through the lens of constrained optimization allows us to leverage tools from stochastic approximation theory to establish the asymptotic normality of the estimated parameters. Existing work typically provides fairness guarantees either in expectation or for the exact minimizer of the constrained objective \citep{del2020review, celis2019classification}, without accounting for the stochasticity induced by the optimization algorithm itself. To construct CIs for fairness in practice, we develop an easily parallelizable online multiplier bootstrap procedure. In doing so, we also extend theoretical guarantees for online bootstrap methods from unconstrained {SGD} to the constrained optimization setting which may be of independent interest. We illustrate the effectiveness of our approach through extensive simulations and experiments on benchmark datasets.} }
Endnote
%0 Conference Paper %T Fairness Uncertainty Quantification: A Constrained Stochastic Optimization Perspective %A Abhishek Roy %A Prasant Mohapatra %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-roy26b %I PMLR %P 5845--5865 %U https://proceedings.mlr.press/v337/roy26b.html %V 337 %X In this paper, we construct confidence interval (CI) for the test-unfairness of a group-fairness aware classifier trained by Stochastic Gradient Descent ({SGD}) type algorithms. Since these algorithms are almost invariably used to train modern machine learning models, the learned parameters—and consequently their fairness—are inherently random. We quantify this randomness, which can have far-reaching consequences, especially for sensitive applications. Viewing fairness-aware classification through the lens of constrained optimization allows us to leverage tools from stochastic approximation theory to establish the asymptotic normality of the estimated parameters. Existing work typically provides fairness guarantees either in expectation or for the exact minimizer of the constrained objective \citep{del2020review, celis2019classification}, without accounting for the stochasticity induced by the optimization algorithm itself. To construct CIs for fairness in practice, we develop an easily parallelizable online multiplier bootstrap procedure. In doing so, we also extend theoretical guarantees for online bootstrap methods from unconstrained {SGD} to the constrained optimization setting which may be of independent interest. We illustrate the effectiveness of our approach through extensive simulations and experiments on benchmark datasets.
APA
Roy, A. & Mohapatra, P.. (2026). Fairness Uncertainty Quantification: A Constrained Stochastic Optimization Perspective. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:5845-5865 Available from https://proceedings.mlr.press/v337/roy26b.html.

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