Private Model Personalization Revisited

We study model personalization under user-level differential privacy (DP) in the shared representation framework. In this problem, there are n users whose data is statistically heterogeneous, and their optimal parameters share an unknown embedding U * ∈ R d×k that maps the user parameters in R d to low-dimensional representations in R k , where k ≪ d. Our goal is to privately recover the shared embedding and the local low-dimensional representations with small excess risk in the federated setting. We propose a private, efficient federated learning algorithm to learn the shared embedding based on the FedRep algorithm in [CHM+21]. Unlike [CHM+21], our algorithm satisfies differential privacy, and our results hold for the case of noisy labels. In contrast to prior work on private model personalization [JRS+21], our utility guarantees hold under a larger class of users' distributions (sub-Gaussian instead of Gaussian distributions). Additionally, in natural parameter regimes, we improve the privacy error term in [JRS+21] by a factor of O(dk). Next, we consider the binary classification setting. We present an information-theoretic construction to privately learn the shared embedding and derive a margin-based accuracy guarantee that is independent of d. Our method utilizes the Johnson-Lindenstrauss transform to reduce the effective dimensions of the shared embedding and the users' data. This result shows that dimension-independent risk bounds are possible in this setting under a margin loss.