  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.
