Improving Differentially Private SGD via Randomly Sparsified Gradients
This work addresses efficiency and privacy trade-offs in differentially private deep learning, offering an incremental improvement to DP-SGD for applications requiring rigorous privacy guarantees.
The paper tackles the performance limitations of Differentially Private Stochastic Gradient Descent (DP-SGD) by introducing random gradient sparsification before clipping and noisification, which theoretically reduces the convergence bound and empirically improves performance in various DP-SGD frameworks, with benefits including reduced communication costs and enhanced privacy against reconstruction attacks.
Differentially private stochastic gradient descent (DP-SGD) has been widely adopted in deep learning to provide rigorously defined privacy, which requires gradient clipping to bound the maximum norm of individual gradients and additive isotropic Gaussian noise. With analysis of the convergence rate of DP-SGD in a non-convex setting, we identify that randomly sparsifying gradients before clipping and noisification adjusts a trade-off between internal components of the convergence bound and leads to a smaller upper bound when the noise is dominant. Additionally, our theoretical analysis and empirical evaluations show that the trade-off is not trivial but possibly a unique property of DP-SGD, as either canceling noisification or gradient clipping eliminates the trade-off in the bound. This observation is indicative, as it implies DP-SGD has special inherent room for (even simply random) gradient compression. To verify the observation and utilize it, we propose an efficient and lightweight extension using random sparsification (RS) to strengthen DP-SGD. Experiments with various DP-SGD frameworks show that RS can improve performance. Additionally, the produced sparse gradients of RS exhibit advantages in reducing communication cost and strengthening privacy against reconstruction attacks, which are also key problems in private machine learning.