Stabilization of Perturbed Loss Function: Differential Privacy without Gradient Noise

TL;DR

SPOF introduces a novel differentially private training method that perturbs a stabilized polynomial approximation of the loss function, enhancing efficiency, stability, and robustness in multi-user privacy scenarios.

Contribution

The paper presents SPOF, a new privacy-preserving training mechanism that avoids gradient noise, improving computational efficiency and robustness over traditional DP-SGD methods.

Findings

SPOF achieves up to 3.5% higher accuracy than DP-SGD.

SPOF reduces training time by up to 57.2%.

SPOF maintains stability under environmental noise.

Abstract

We propose SPOF (Stabilization of Perturbed Loss Function), a differentially private training mechanism intended for multi-user local differential privacy (LDP). SPOF perturbs a stabilized Taylor expanded polynomial approximation of a model's training loss function, where each user's data is privatized by calibrated noise added to the coefficients of the polynomial. Unlike gradient-based mechanisms such as differentially private stochastic gradient descent (DP-SGD), SPOF does not require injecting noise into the gradients of the loss function, which improves both computational efficiency and stability. This formulation naturally supports simultaneous privacy guarantees across all users. Moreover, SPOF exhibits robustness to environmental noise during training, maintaining stable performance even when user inputs are corrupted. We compare SPOF with a multi-user extension of DP-SGD, evaluating both methods in a wireless body area network (WBAN) scenario involving heterogeneous user data and stochastic channel noise from body sensors. Our results show that SPOF achieves, on average, up to 3.5% higher reconstruction accuracy and reduces mean training time by up to 57.2% compared to DP-SGD, demonstrating superior privacy-utility trade-offs in multi-user environments.