DP-$\lambda$CGD: Efficient Noise Correlation for Differentially Private Model Training

Differentially private stochastic gradient descent (DP-SGD) is the gold standard for training machine learning models with formal differential privacy guarantees. Several recent extensions improve its accuracy by introducing correlated noise across training iterations. Matrix factorization mechanisms are a prominent example, but they can require storing previously added noise vectors, leading to substantial memory overhead. In this work, we propose a new algorithm for correlated-noise private training that correlates noise only with the immediately preceding iteration and cancels a tunable portion of it. By regenerating the previous noise using a pseudorandom number generator rather than storing it, our method has essentially the same memory footprint as DP-SGD. We show that the computational overhead is minimal and empirically demonstrate improved accuracy over DP-SGD.