Federated and differentially private estimation of KL divergence

Measuring distribution drifts is a key task in managing distributed, sensitive data, as it underpins a wide range of federated learning and analytics applications. In many practical settings, however, directly sharing such information is either undesirable (e.g., due to privacy concerns) or infeasible (e.g., due to high communication costs). In this work, we present FedPriKL, a novel method for estimating the KL divergence of data across federated computational models under differential privacy (DP) guarantees. We establish its theoretical properties, showing that FedPriKL is unbiased with low and bounded sensitivity and variance, thereby ensuring strong utility under DP. In addition, we present an empirical study that explores parameter choices to optimize accuracy while minimizing communication overhead. Our experiments demonstrate that FedPriKL achieves accuracy comparable to a similar sampling-based non-private estimator, while delivering greater stability and accuracy than a baseline variant in which users perturb their data locally to obtain privacy guarantees.