Abstract: In this talk we will review some recent results on the Bayesian approach for bilevel programming. We focus our attention in linear bilevel programming and the beliefs induced by uncertain lower-level costs. We show that such problems (and their sample average approximations) can be written as piecewise linear minimization problems over a polyhedral complex induced by the feasible region of the bilevel formulation. We will describe two algorithms to solve the problem: a deterministic one based on vertex enumeration, and a Monte-Carlo algorithm based on sampling full-dimensional elements of the aforementioned polyhedral complex.

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