Amplifying R\'enyi Differential Privacy via Shuffling

Differential privacy is a useful tool to build machine learning models which do not release too much information about the training data. We study the R\'enyi differential privacy of stochastic gradient descent when each training example is sampled without replacement (also known as cyclic SGD). Cyclic SGD is typically faster than traditional SGD and is the algorithm of choice in large-scale implementations. We recover privacy guarantees for cyclic SGD which are competitive with those known for sampling with replacement. Our proof techniques make no assumptions on the model or on the data and are hence widely applicable.