Stabilization of Perturbed Loss Function: Differential Privacy without Gradient Noise
This addresses privacy-utility trade-offs in multi-user environments like wireless body area networks, offering an incremental improvement over gradient-based methods.
The paper tackles the problem of differentially private training in multi-user local settings by proposing SPOF, which perturbs a polynomial approximation of the loss function instead of gradients, resulting in up to 3.5% higher accuracy and 57.2% faster training compared to DP-SGD.
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.