Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets

ArXi:2605.09209v1 Announce Type: cross We study optimistic bilevel optimization when the lower-level problem has a non-isolated manifold of minimizers. In this setting, the hyper-objective may be non-differentiable because the upper-level criterion must choose among multiple lower-level solutions. Under a local Polyak--{\L}ojasiewicz (P{\L}) condition, we show that differentiability does not require the lower-level solution set to be a singleton: uniqueness of the optimistic selection is sufficient.