  We study convergence lower bounds of without-replacement stochastic gradient
descent (SGD) for solving smooth (strongly-)convex finite-sum minimization
problems. Unlike most existing results focusing on final iterate lower bounds
in terms of the number of components $n$ and the number of epochs $K$, we seek
bounds for arbitrary weighted average iterates that are tight in all factors
including the condition number $\kappa$. For SGD with Random Reshuffling, we
present lower bounds that have tighter $\kappa$ dependencies than existing
bounds. Our results are the first to perfectly close the gap between lower and
upper bounds for weighted average iterates in both strongly-convex and convex
cases. We also prove weighted average iterate lower bounds for arbitrary
permutation-based SGD, which apply to all variants that carefully choose the
best permutation. Our bounds improve the existing bounds in factors of $n$ and
$\kappa$ and thereby match the upper bounds shown for a recently proposed
algorithm called GraB.
