Multi-Agent Privacy Game in Federated Learning: A Unified Mean-Field View

Record-level differential privacy exposes a structural misalignment in personalized federated learning when client-specific variation is low-dimensional while training repeatedly releases high-dimensional updates. In this paper, we address this misalignment by releasing a private client context once and confining repeated adaptation to a fixed coefficient space. Beyond dimensionality reduction, the factorized generator induces an adaptive optimization geometry that reshapes noisy updates, and controlled ablations show that most of its private-training gain is retained by radial evolution. To further reduce the communication cost, we realize the Gaussian mechanism for coefficient updates directly through variable-length quantization with finite expected code length, so that the quantization error itself serves as the required privacy perturbation rather than extra distortion. Across MNIST and CIFAR-10, our design matches or outperforms full-model private adaptation across privacy budgets and client heterogeneity, while reducing protected uplink by a factor of 2.67 at $\varepsilon=16$ on CIFAR-10 with comparable future-client accuracy.

The growing development of artificial intelligence based solutions, together with privacy legislation, has driven the rise of the so-called privacy preserving machine learning architectures, such as federated learning. While federated learning enables model training on decentralized data preventing their sharing and centralization, it still faces several challenges related to data integrity and privacy. This paper presents a comprehensive privacy preserving federated learning workflow for sensitive tabular data, including anonymization and differential privacy techniques. We also introduce a formal definition for the concept of client drift, together with ways of detecting it to mitigate poisoning attacks. Then, we detail a complete methodology for assigning personalized privacy budgets for global differential privacy to the different clients participating in the network, based on a re-identification risk metric. The proposed methodology is presented and tested on an openly available dataset of medical records. Within the experimental setup we show that the approach based on personalized budgets, compared to the architecture including global differential privacy with fixed privacy budget, achieves a better model performance in terms of two error metrics.

This work focuses on the question of learning from a large number of devices with each device holding only a single sample of data. Several real-world applications exist to this one sample per client setup up including learning from fitness trackers, data/app usage aggregators, body-worn sensing devices, and daily event monitors to name a few. When a client has only one sample, the standard federated learning paradigm breaks down as a local update based on that single point is far from being useful, especially in the earlier rounds for estimation of the model coefficients. This utility is further weakened by the privacy-inducing noise applied at every round. This work caters to this problem to enable such clients to collaboratively contribute to effectively learn a global model without leaking the privacy of their data. The proposed approach injects a single, carefully calibrated noisy perturbation to transform the sample at each client, followed by a post-processed representation which is shared with the server. These representations aggregated at the server are processed to obtain an unbiased gradient update that in expectation matches the non-private centralized gradient while preserving data privacy. This approach is different than traditional private federated learning, where the communication payloads involve model coefficients as opposed to privately transformed data samples. This method enables devices with extremely limited data to collaborate and learn accurate, privacy-preserving models without requiring large local datasets or sacrificing individual privacy.