Participation-Dependent Privacy Preservation in Cross-Silo Federated Learning

In cross-silo federated learning (FL), clients of common interest cooperatively train a global model without sharing local sensitive data, but they still face potential privacy leakage due to privacy threats from malicious attackers. Although some articles have proposed effective privacy-preserving mechanisms for FL (such as differential privacy (DP)), clients in cross-silo FL are usually different companies or organizations who may behave selfishly to optimize their own benefits. In this article, we study DP-based cross-silo FL where clients selfishly decide their participation levels (i.e., data sizes for model trainings) and privacy leakage tolerance levels to trade off between model accuracy loss and privacy loss, and we model clients’ interactions as a participation-dependent privacy preservation game. It is challenging to analyze the game since the comprehensive impact of participation levels and privacy leakage tolerance levels on model accuracy is unclear and the behaviors of heterogeneous clients are coupled in a highly complex manner. To capture the impact of participation and privacy preservation behaviors, we first characterize the optimality gap of DP-based cross-silo FL for both convex and non-convex models, where the privacy leakage tolerance levels and the participation levels are coupled nonlinearly. We model clients’ costs based on the optimality gap, and prove that clients’ selfish participation-dependent privacy preservation game is a potential game. To analyze the optimal strategies of heterogeneous clients in a stable state, we derive the closed-form expression for the unique Nash equilibrium (NE), where clients may choose full participation or partial participation, and the equilibrium privacy preservation strategy depends on clients’ accuracy-privacy preference ratios. We analyze the social efficiency of the NE by calculating the price of anarchy (PoA) and show that the PoA increases with the number of clients and the heterogeneity of clients’ model accuracy preferences. To improve the social efficiency achieved at equilibrium, we design a socially efficient incentive mechanism that allows clients with large model accuracy preferences to compensate clients with small model accuracy preferences. Extensive experiments verify our theoretical results for both the convex and non-convex models as well as both the i.i.d. data distribution case and the non-i.i.d. data distribution case.

I. Introduction

With the rapid development of the Internet of Things (IoT), various sensing devices and mobile phones generate enormous data, which exist in the form of data islands [1]. The traditional solution to the data islands problem is to collect data and train models on a central server, which may cause data leakage during data collection. Federated learning (FL), proposed by Google [2], is a distributed learning method without data collection. In FL, clients collaborate with each other to train a model under the orchestration of a central server, as shown in Fig. 1. Specifically, each client trains a local model with its personal local data and uploads the local model updates to the central server for aggregation. The server then updates the global model and resends it to clients. The model training proceeds until the global model converges or the training process reaches a specified stop condition. There are in general two categories of FL: cross-device FL and cross-silo FL [3]. In cross-device FL, a central server initiates the FL process and incentivizes clients (who are usually a large number of devices) to participate in model training. In cross-silo FL, clients of common interest (who are usually organizations or companies) initiate the FL process and pay a central server for global aggregation to obtain a model.