M-estimation Under User-Level Local Privacy Constraints

01.03.2024 11:15 – 12:15

RESEARCH CENTER FOR STATISTICS SEMINAR / ABSTRACT

We consider a first order convex optimization-based framework for computing M-estimators under local differential privacy (LDP) constraints. We assume a group of users communicates with an untrusted central server that learns the parameters of an underlying model. Furthermore, each user contributes multiple data points to the server. Contrary to most works that aim to protect a single data point, we focus on user-level privacy, that aims to protect the entire set of data points belonging to a user. Our main algorithm is a noisy version of the standard gradient descent algorithm, combined with a user-level LDP mean estimation procedure to privately compute the average gradient across users at each step. We characterize the rate of convergence for parameter estimation under user-level local privacy constraints, and show that it improves with the number of users and the number of samples per user.

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