Privacy as Commodity: MFG-RegretNet for Large-Scale Privacy Trading in Federated Learning

TL;DR

This paper introduces MFG-RegretNet, a deep-learning-based auction mechanism for privacy trading in federated learning, addressing privacy risks and incentivizing high-quality client contributions through a market formalized as a Privacy Auction Game.

Contribution

It proposes a novel mean-field game approximation combined with differentiable mechanism design to efficiently compute equilibria in large-scale privacy trading markets.

Findings

MFG-RegretNet outperforms baselines in incentive compatibility, revenue, and social welfare.

The approach reduces computational complexity from quadratic to linear in the number of clients.

Experiments on MNIST and CIFAR-10 show maintained model accuracy with improved privacy incentives.

Abstract

Federated Learning (FL) has emerged as a prominent paradigm for privacy-preserving distributed machine learning, yet two fundamental challenges hinder its large-scale adoption. First, gradient inversion attacks can reconstruct sensitive training data from uploaded model updates, so privacy risk persists even when raw data remain local. Second, without adequate monetary compensation, rational clients have little incentive to contribute high-quality gradients, limiting participation at scale. To address these challenges, a privacy trading market is developed in which clients sell their differential privacy budgets as a commodity and receive explicit economic compensation for privacy sacrifice. This market is formalized as a Privacy Auction Game (PAG), and the existence of a Bayesian Nash Equilibrium is established under dominant-strategy incentive compatibility (DSIC), individual rationality (IR), and budget feasibility. To overcome the NP-hard, high-dimensional Nash Equilibrium computation at scale, \textit{MFG-RegretNet} is introduced as a deep-learning-based auction mechanism that combines mean-field game (MFG) approximation with differentiable mechanism design. The MFG reduction lowers per-round computational complexity from $\mathcal{O}(N^2 \log N)$ to $\mathcal{O}(N)$ while incurring only an $\mathcal{O}(N^{-1/2})$ equilibrium approximation gap. Extensive experiments on MNIST and CIFAR-10 demonstrate that MFG-RegretNet outperforms state-of-the-art baselines in incentive compatibility, auction revenue, and social welfare, while maintaining competitive downstream FL model accuracy.