  In this paper, we provide a generic anytime lower bounding procedure for
minmax regret optimization problems. We show that the lower bound obtained is
always at least as accurate as the lower bound recently proposed by Chassein
and Goerigk (2015). This lower bound can be viewed as the optimal value of a
linear programming relaxation of a mixed integer programming formulation of
minmax regret optimization, but the contribution of the paper is to compute
this lower bound via a double oracle algorithm (McMahan et al., 2003) that we
specify. The double oracle algorithm is designed by relying on a game theoretic
view of robust optimization, similar to the one developed by Mastin et al.
(2015), and it can be efficiently implemented for any minmax regret
optimization problem whose standard version is "easy". We describe how to
efficiently embed this lower bound in a branch and bound procedure. Finally, we
apply our approach to the robust shortest path problem. Our numerical results
show a significant gain in the computation times compared to previous
approaches in the literature.
