  In this paper, we quantitative convergence in $W_2$ for a family of
Langevin-like stochastic processes that includes stochastic gradient descent
and related gradient-based algorithms. Under certain regularity assumptions, we
show that the iterates of these stochastic processes converge to an invariant
distribution at a rate of $\tilde{O}\lrp{1/\sqrt{k}}$ where $k$ is the number
of steps; this rate is provably tight up to log factors. Our result reduces to
a quantitative form of the classical Central Limit Theorem in the special case
when the potential is quadratic.
