On the Condition Number Dependency in Bilevel Optimization
Quick summary
arXiv:2511.22331v4 Announce Type: replace-cross Abstract: Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\epsilon$-stationary point with first-order methods when the upper-level problem is nonconvex, and the lower-level problem is strongly convex. Recent works achieve a $\tilde{\mathcal{O}}(\bar \kappa_y^{7/2} \epsilon^{-2})$ upper bound that is near-optimal in $\epsilon$. In this work, we establish a new $\Omega(\kappa_y^{5/2} \epsilon^{-2})$ l
Key takeaways
- arXiv:2511.22331v4 Announce Type: replace-cross Abstract: Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem.
- We study the oracle complexity of finding an $\epsilon$-stationary point with first-order methods when the upper-level problem is nonconvex, and the lower-level problem is strongly convex.
- Recent works achieve a $\tilde{\mathcal{O}}(\bar \kappa_y^{7/2} \epsilon^{-2})$ upper bound that is near-optimal in $\epsilon$.
Why it matters
“On the Condition Number Dependency in Bilevel Optimization” highlights the need for repeatable measurement rather than a single impressive demonstration. Independent validation across datasets and clearly stated limitations determine whether a result can guide product decisions.
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