We consider bilevel optimization problems in which the leader has no or only partial knowledge about the objective function of the follower. The studied setting is a sequential one in which the bilevel game is played repeatedly. This allows the leader to learn the objective function of the follower over time. We focus on two methods: a multiplicative weight update (MWU) method and one based on the lower-level's KKT conditions that are used in the fashion of inverse optimization. The MWU method requires less assumptions but the convergence guarantee is also only on the objective function values, whereas the inverse KKT method requires stronger assumptions but actually allows to learn the objective function itself. The applicability of the proposed methods is shown using two case studies. First, we study a repeatedly played continuous knapsack interdiction problem and, second, a sequential bilevel pricing game in which the leader needs to learn the utility function of the follower.
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