Differentially Private Model Merging

In machine learning applications, privacy requirements during inference or deployment time could change constantly due to varying policies, regulations, or user experience. In this work, we aim to generate a magnitude of models to satisfy any target differential privacy (DP) requirement without additional training steps, given a set of existing models trained on the same dataset with different privacy/utility tradeoffs. We propose two post processing techniques, namely random selection and linear combination, to output final private models satisfying any target privacy parameter. We provide privacy accounting of these approaches from the lens of R\'enyi DP and privacy loss distributions for general problems. In a case study on private mean estimation, we precisely characterize the privacy/utility results and theoretically establish the superiority of linear combination over random selection. Empirically, we validate our approaches and analyses on several models and both synthetic and real-world datasets.