  We study Nesterov's accelerated gradient method with constant step-size and
momentum parameters in the stochastic approximation setting (unbiased gradients
with bounded variance) and the finite-sum setting (where randomness is due to
sampling mini-batches). To build better insight into the behavior of Nesterov's
method in stochastic settings, we focus throughout on objectives that are
smooth, strongly-convex, and twice continuously differentiable. In the
stochastic approximation setting, Nesterov's method converges to a neighborhood
of the optimal point at the same accelerated rate as in the deterministic
setting. Perhaps surprisingly, in the finite-sum setting, we prove that
Nesterov's method may diverge with the usual choice of step-size and momentum,
unless additional conditions on the problem related to conditioning and data
coherence are satisfied. Our results shed light as to why Nesterov's method may
fail to converge or achieve acceleration in the finite-sum setting.
