  In this work, we introduce two algorithmic frameworks, named Bregman
extragradient method and Bregman extrapolation method, for solving saddle point
problems. The proposed frameworks not only include the well-known extragradient
and optimistic gradient methods as special cases, but also generate new
variants such as sparse extragradient and extrapolation methods. With the help
of the recent concept of relative Lipschitzness and some Bregman distance
related tools, we are able to show certain upper bounds in terms of Bregman
distances for ``regret" measures. Further, we use those bounds to deduce the
convergence rate of $\cO(1/k)$ for the Bregman extragradient and Bregman
extrapolation methods applied to solving smooth convex-concave saddle point
problems. Our theory recovers the main discovery made in [Mokhtari et al.
(2020), SIAM J. Optim., 20, pp. 3230-3251] for more general algorithmic
frameworks with weaker assumptions via a conceptually different approach.
