On the Condition Number Dependency in Bilevel Optimization
📰 ArXiv cs.AI
Learn how condition number affects bilevel optimization and apply first-order methods to find an epsilon-stationary point in nonconvex upper-level problems
Action Steps
- Apply first-order methods to bilevel optimization problems with nonconvex upper-level and strongly convex lower-level problems
- Analyze the condition number of the lower-level problem to understand its impact on the oracle complexity
- Use the condition number to determine the appropriate step size for the first-order method
- Implement the bilevel optimization algorithm using a programming language such as Python or MATLAB
- Test the algorithm on a variety of problems to evaluate its performance and robustness
Who Needs to Know This
Researchers and practitioners working on bilevel optimization problems, particularly those with nonconvex upper-level and strongly convex lower-level problems, can benefit from understanding the condition number dependency to improve their optimization methods
Key Insight
💡 The condition number of the lower-level problem affects the oracle complexity of bilevel optimization algorithms
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Bilevel optimization: understand condition number dependency to improve first-order methods #bileveloptimization #optimization
Key Takeaways
Learn how condition number affects bilevel optimization and apply first-order methods to find an epsilon-stationary point in nonconvex upper-level problems
Full Article
Title: On the Condition Number Dependency in Bilevel Optimization
Abstract:
arXiv:2511.22331v2 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 (Ji et al., ICML 2021; Arbel and Mairal, ICLR 2022; Chen et al., JMLR 2025) achieve a $\
Abstract:
arXiv:2511.22331v2 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 (Ji et al., ICML 2021; Arbel and Mairal, ICLR 2022; Chen et al., JMLR 2025) achieve a $\
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