Ranking Distance Metric for Privacy Budget in Distributed Learning of Finite Embedding Data

Federated Learning (FL) is a collective of distributed learning paradigm that aims to preserve privacy in data. Recent studies have shown FL models to be vulnerable to reconstruction attacks that compromise data privacy by inverting gradients computed on confidential data. To address the challenge of defending against these attacks, it is common to employ methods that guarantee data confidentiality using the principles of Differential Privacy (DP). However, in many cases, especially for machine learning models trained on unstructured data such as text, evaluating privacy requires to consider also the finite space of embedding for client’s private data. In this study, we show how privacy in a distributed FL setup is sensitive to the underlying finite embeddings of the confidential data. We show that privacy can be quantified for a client batch that uses either noise, or a mixture of finite embeddings, by introducing a normalised rank distance ( \(d_{rank}\) ). This measure has the advantage of taking into account the size of a finite vocabulary embedding, and align the privacy budget to a partitioned space. We further explore the impact of noise and client batch size on the privacy budget and compare it to the standard \(\epsilon \) derived from Local-DP.