Decision bounding problems for two-stage distributionally robust stochastic bilevel optimization

Distributionally robust optimization (DRO) becomes a hot research topic in stochastic programming (SP) due to its characteristic for solving SP problems with incomplete distribution information. In this paper, we study a two-stage distributionally robust stochastic bilevel optimization problem (TDRBO) under the moment uncertainty. The TDRBO problem has a complicated optimization structure and is intractable. To this end, we first present the corresponding robust optimistic and pessimistic models as the bounds of the TDRBO problem. Then we use the decision rule approach to handle the bounded optimization problems under two situations of fixed recourse and random recourse. Finally, we obtain the tractable bounded optimization problems of the TDRBO problem. Some theoretical results are established and the numerical results are presented, showing that the approaches proposed in this paper are reasonable and effective.