  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. In this paper, we develop new risk-neutral
and risk-averse formulations, address their main computational challenges, and
develop the corresponding deterministic and stochastic gradient-based
algorithms.
