  We study the last-iterate convergence of variance reduction methods for
extragradient (EG) algorithms for a class of variational inequalities
satisfying error-bound conditions. Previously, last-iterate linear convergence
was only known under strong monotonicity. We show that EG algorithms with
SVRG-style variance reduction, denoted SVRG-EG, attain last-iterate linear
convergence under a general error-bound condition much weaker than strong
monotonicity. This condition captures a broad class of non-strongly monotone
problems, such as bilinear saddle-point problems commonly encountered in
two-player zero-sum Nash equilibrium computation. Next, we establish linear
last-iterate convergence of SVRG-EG with an improved guarantee under the weak
sharpness assumption. Furthermore, motivated by the empirical efficiency of
increasing iterate averaging techniques in solving saddle-point problems, we
also establish new convergence results for SVRG-EG with such techniques.
