A Differentially Private Weighted Empirical Risk Minimization Procedure and its Application to Outcome Weighted Learning

It is commonplace to use data containing personal information to build predictive models in the framework of empirical risk minimization (ERM). While these models can be highly accurate in prediction, results obtained from these models with the use of sensitive data may be susceptible to privacy attacks. Differential privacy (DP) is an appealing framework for addressing such data privacy issues by providing mathematically provable bounds on the privacy loss incurred when releasing information from sensitive data. Previous work has primarily concentrated on applying DP to unweighted ERM. We consider an important generalization to weighted ERM (wERM). In wERM, each individual's contribution to the objective function can be assigned varying weights. In this context, we propose the first differentially private wERM algorithm, backed by a rigorous theoretical proof of its DP guarantees under mild regularity conditions. Extending the existing DP-ERM procedures to wERM paves a path to deriving privacy-preserving learning methods for individualized treatment rules, including the popular outcome weighted learning (OWL). We evaluate the performance of the DP-wERM application to OWL in a simulation study and in a real clinical trial of melatonin for sleep health. All empirical results demonstrate the viability of training OWL models via wERM with DP guarantees while maintaining sufficiently useful model performance. Therefore, we recommend practitioners consider implementing the proposed privacy-preserving OWL procedure in real-world scenarios involving sensitive data.