← Back to all news
arXiv Machine Learning By Johannes O. Royset

On Stability in Optimistic Bilevel Optimization

Read the original on arXiv Machine Learning →

The paper addresses instability in bilevel optimization solutions when problem data changes. It proposes a lifted formulation for the optimistic setting that remains stable under mild assumptions, without requiring convexity or smoothness. The approach accommodates integer restrictions and disjunctive constraints, relies on pointwise and local calmness of the lower-level problem, and offers computational advantages including an outer approximation algorithm.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Sep 2

Disciplined Bilevel Programming

arXiv:2609.00644v1 Announce Type: cross Abstract: Bilevel optimization provides a natural modeling language for hierarchical decision problems. However, applying existing numerical solvers usually re...

By Hao Zhu, Joschka Boedecker
More like this →
arXiv Machine Learning
Jul 24

Non-Stationary Functional Bilevel Optimization

arXiv:2601. 15363v2 Announce Type: replace-cross Abstract: Functional bilevel optimization (FBO) provides a powerful framework for hierarchical learning in function spaces, yet current methods are limited to static offline settings and perform suboptimally in online, non-stationary scenarios.

By Jason Bohne, Ieva Petrulionyte, Michael Arbel, Julien Mairal, Pawe{\l} Polak
reinforcement-learning
More like this →
arXiv Machine Learning
1d ago

Optimal Stochastic Bilevel Optimization with First-Order Oracles

The paper investigates nonconvex–strongly-convex bilevel optimization using a stochastic first-order oracle. It introduces MRT‑FD, a single-loop first‑order algorithm that tracks the upper-level variable, the lower-level solution, and an auxiliary response from implicit differentiation, updating all variables in each iteration and approximating second‑order derivative actions via order‑p finite differences. For any fixed finite smoothness order p ≥ 1, MRT‑FD achieves an ε‑stationary point with O(ε^{‑4‑2/p}) stochastic gradient queries, and the authors prove a matching Ω(ε^{‑4‑2/p}) lower bound, thereby closing the complexity gap in this setting.

By Linxuan Pan, Junchi Yang
More like this →