Concentrated Differentially Private Gradient Descent with Adaptive per-Iteration Privacy Budget
This work addresses the need for more efficient privacy-preserving optimization in machine learning, though it is incremental as it builds on existing differential privacy frameworks.
The paper tackles the problem of improving differentially private gradient descent by adaptively allocating privacy budget per iteration, showing that it outperforms prior algorithms for model fitting and is competitive with state-of-the-art methods under weaker privacy definitions.
Iterative algorithms, like gradient descent, are common tools for solving a variety of problems, such as model fitting. For this reason, there is interest in creating differentially private versions of them. However, their conversion to differentially private algorithms is often naive. For instance, a fixed number of iterations are chosen, the privacy budget is split evenly among them, and at each iteration, parameters are updated with a noisy gradient. In this paper, we show that gradient-based algorithms can be improved by a more careful allocation of privacy budget per iteration. Intuitively, at the beginning of the optimization, gradients are expected to be large, so that they do not need to be measured as accurately. However, as the parameters approach their optimal values, the gradients decrease and hence need to be measured more accurately. We add a basic line-search capability that helps the algorithm decide when more accurate gradient measurements are necessary. Our gradient descent algorithm works with the recently introduced zCDP version of differential privacy. It outperforms prior algorithms for model fitting and is competitive with the state-of-the-art for $(ε,δ)$-differential privacy, a strictly weaker definition than zCDP.