2016/02/04 by Hugo Gilbert, Gilbert, Hugo, Olivier Spanjaard +1
Decision Sciences · Economics, Econometrics and Finance · Engineering · Mathematics · #90C27 #Advanced Bandit Algorithms Research #Advanced Optimization Algorithms Research #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #G.1.6 #G.2.2 #G.4 #Monetary Policy and Economic Impact #Risk and Portfolio Optimization #Water resources management and optimization
paper · pdf · doi:10.48550/arxiv.1602.01764
openalex publication_date 2016/02/04 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this paper, we provide a generic anytime lower bounding procedure for\nminmax regret optimization problems. We show that the lower bound obtained is\nalways at least as accurate as the lower bound recently proposed by Chassein\nand Goerigk (2015). This lower bound can be viewed as the optimal value of a\nlinear programming relaxation of a mixed integer programming formulation of\nminmax regret optimization, but the contribution of the paper is to compute\nthis lower bound via a double oracle algorithm (McMahan et al., 2003) that we\nspecify. The double oracle algorithm is designed by relying on a game theoretic\nview of robust optimization, similar to the one developed by Mastin et al.\n(2015), and it can be efficiently implemented for any minmax regret\noptimization problem whose standard version is "easy". We describe how to\nefficiently embed this lower bound in a branch and bound procedure. Finally, we\napply our approach to the robust shortest path problem. Our numerical results\nshow a significant gain in the computation times compared to previous\napproaches in the literature.\n