  The main purpose of this paper is to propose a variance-based Bregman
extragradient algorithm with line search for solving stochastic variational
inequalities, which is robust with respect an unknown Lipschitz constant. We
prove the almost sure convergence of the algorithm by a more concise and
effective method instead of using the supermartingale convergence theorem.
Furthermore, we obtain not only the convergence rate $\mathcal{O}(1/k)$ with
the gap function when $X$ is bounded, but also the same convergence rate in
terms of the natural residual function when $X$ is unbounded. Under the Minty
variational inequality condition, we derive the iteration complexity
$\mathcal{O}(1/\varepsilon)$ and the oracle complexity
$\mathcal{O}(1/\varepsilon^2)$ in both cases. Finally, some numerical results
demonstrate the superiority of the proposed algorithm.
