Private Rate-Constrained Optimization with Applications to Fair Learning

TL;DR

This paper introduces RaCO-DP, a differentially private algorithm for constrained optimization in fair machine learning, addressing inter-sample dependencies and demonstrating superior fairness-utility trade-offs.

Contribution

We develop RaCO-DP, a novel DP-SGDA algorithm for rate-constrained problems, with convergence analysis and empirical validation on fairness tasks.

Findings

RaCO-DP effectively handles rate constraints under differential privacy.

The method achieves better fairness-utility trade-offs than existing approaches.

Empirical results demonstrate Pareto dominance in fairness and utility.

Abstract

Many problems in trustworthy ML can be formulated as minimization of the model error under constraints on the prediction rates of the model for suitably-chosen marginals, including most group fairness constraints (demographic parity, equality of odds, etc.). In this work, we study such constrained minimization problems under differential privacy (DP). Standard DP optimization techniques like DP-SGD rely on the loss function's decomposability into per-sample contributions. However, rate constraints introduce inter-sample dependencies, violating the decomposability requirement. To address this, we develop RaCO-DP, a DP variant of the Stochastic Gradient Descent-Ascent (SGDA) algorithm which solves the Lagrangian formulation of rate constraint problems. We demonstrate that the additional privacy cost of incorporating these constraints reduces to privately estimating a histogram over the mini-batch at each optimization step. We prove the convergence of our algorithm through a novel analysis of SGDA that leverages the linear structure of the dual parameter. Finally, empirical results on learning under group fairness constraints demonstrate that our method Pareto-dominates existing private learning approaches in fairness-utility trade-offs.