ADP-VRSGP: Decentralized Learning with Adaptive Differential Privacy via Variance-Reduced Stochastic Gradient Push

Differential privacy is widely employed in decentralized learning to safeguard sensitive data by introducing noise into model updates. However, existing approaches that use fixed-variance noise often degrade model performance and reduce training efficiency. To address these limitations, we propose a novel approach called decentralized learning with adaptive differential privacy via variance-reduced stochastic gradient push (ADP-VRSGP). This method dynamically adjusts both the noise variance and the learning rate using a stepwise-decaying schedule, which accelerates training and enhances final model performance while providing node-level personalized privacy guarantees. To counteract the slowed convergence caused by large-variance noise in early iterations, we introduce a progressive gradient fusion strategy that leverages historical gradients. Furthermore, ADP-VRSGP incorporates decentralized push-sum and aggregation techniques, making it particularly suitable for time-varying communication topologies. Through rigorous theoretical analysis, we demonstrate that ADP-VRSGP achieves robust convergence with an appropriate learning rate, significantly improving training stability and speed. Experimental results validate that our method outperforms existing baselines across multiple scenarios, highlighting its efficacy in addressing the challenges of privacy-preserving decentralized learning.