  In empirical risk optimization, it has been observed that stochastic gradient
implementations that rely on random reshuffling of the data achieve better
performance than implementations that rely on sampling the data uniformly.
Recent works have pursued justifications for this behavior by examining the
convergence rate of the learning process under diminishing step-sizes. This
work focuses on the constant step-size case and strongly convex loss function.
In this case, convergence is guaranteed to a small neighborhood of the
optimizer albeit at a linear rate. The analysis establishes analytically that
random reshuffling outperforms uniform sampling by showing explicitly that
iterates approach a smaller neighborhood of size $O(\mu^2)$ around the
minimizer rather than $O(\mu)$. Furthermore, we derive an analytical expression
for the steady-state mean-square-error performance of the algorithm, which
helps clarify in greater detail the differences between sampling with and
without replacement. We also explain the periodic behavior that is observed in
random reshuffling implementations.
