  We study stochastic gradient descent {\em without replacement} (\sgdwor) for
smooth convex functions. \sgdwor is widely observed to converge faster than
true \sgd where each sample is drawn independently {\em with replacement}
\cite{bottou2009curiously} and hence, is more popular in practice. But it's
convergence properties are not well understood as sampling without replacement
leads to coupling between iterates and gradients. By using method of
exchangeable pairs to bound Wasserstein distance, we provide the first
non-asymptotic results for \sgdwor when applied to {\em general smooth,
strongly-convex} functions. In particular, we show that \sgdwor converges at a
rate of $O(1/K^2)$ while \sgd is known to converge at $O(1/K)$ rate, where $K$
denotes the number of passes over data and is required to be {\em large
enough}. Existing results for \sgdwor in this setting require additional {\em
Hessian Lipschitz assumption} \cite{gurbuzbalaban2015random,haochen2018random}.
  For {\em small} $K$, we show \sgdwor can achieve same convergence rate as
\sgd for {\em general smooth strongly-convex} functions. Existing results in
this setting require $K=1$ and hold only for generalized linear models
\cite{shamir2016without}. In addition, by careful analysis of the coupling, for
both large and small $K$, we obtain better dependence on problem dependent
parameters like condition number.
