  We consider stochastic gradient descent algorithms for minimizing a
non-smooth, strongly-convex function. Several forms of this algorithm,
including suffix averaging, are known to achieve the optimal $O(1/T)$
convergence rate in expectation. We consider a simple, non-uniform averaging
strategy of Lacoste-Julien et al. (2011) and prove that it achieves the optimal
$O(1/T)$ convergence rate with high probability. Our proof uses a recently
developed generalization of Freedman's inequality. Finally, we compare several
of these algorithms experimentally and show that this non-uniform averaging
strategy outperforms many standard techniques, and with smaller variance.
