  We consider the generalization error associated with stochastic gradient
descent on a smooth convex function over a compact set. We show the first bound
on the generalization error that vanishes when the number of iterations $T$ and
the dataset size $n$ go to zero at arbitrary rates; our bound scales as
$\tilde{O}(1/\sqrt{T} + 1/\sqrt{n})$ with step-size $\alpha_t = 1/\sqrt{t}$. In
particular, strong convexity is not needed for stochastic gradient descent to
generalize well.
