Private Rate-Constrained Optimization with Applications to Fair Learning
This addresses the problem of ensuring both fairness and privacy in ML models for applications like group fairness, though it is incremental as it builds on existing SGDA techniques.
The paper tackled the problem of optimizing machine learning models under fairness constraints while preserving differential privacy, which is challenging due to inter-sample dependencies from rate constraints. The result was RaCO-DP, a method that Pareto-dominates existing private learning approaches in fairness-utility trade-offs.
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.