Bilevel optimization with a multi-objective lower-level problem: Risk-neutral and risk-averse formulations

Understand

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level.

• Such problems have received little attention in the deterministic case and have never been studied from a stochastic approximation viewpoint despite the recent advances in stochastic methods for single-level, bilevel, and multi-objective optimization.
• To solve bilevel problems with a multi-objective lower level, different approaches can be considered depending on the interpretation of the lower-level optimality.
• An optimistic formulation that was previously introduced for the deterministic case consists of minimizing the upper-level function over all non-dominated lower-level solutions.