Group privacy for personalized federated learning

Federated learning is a type of collaborative machine learning, where participating clients process their data locally, sharing only updates to the collaborative model. This enables to build privacy-aware distributed machine learning models, among others. The goal is the optimization of a statistical model's parameters by minimizing a cost function of a collection of datasets which are stored locally by a set of clients. This process exposes the clients to two issues: leakage of private information and lack of personalization of the model. On the other hand, with the recent advancements in techniques to analyze data, there is a surge of concern for the privacy violation of the participating clients. To mitigate this, differential privacy and its variants serve as a standard for providing formal privacy guarantees. Often the clients represent very heterogeneous communities and hold data which are very diverse. Therefore, aligned with the recent focus of the FL community to build a framework of personalized models for the users representing their diversity, it is also of utmost importance to protect against potential threats against the sensitive and personal information of the clients. $d$-privacy, which is a generalization of geo-indistinguishability, the lately popularized paradigm of location privacy, uses a metric-based obfuscation technique that preserves the spatial distribution of the original data. To address the issue of protecting the privacy of the clients and allowing for personalized model training to enhance the fairness and utility of the system, we propose a method to provide group privacy guarantees exploiting some key properties of $d$-privacy which enables personalized models under the framework of FL. We provide with theoretical justifications to the applicability and experimental validation on real-world datasets to illustrate the working of the proposed method.