Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets
📰 ArXiv cs.AI
Learn to solve bilevel optimization problems with non-isolated manifold lower-level solution sets using the select-then-differentiate approach
Action Steps
- Apply the select-then-differentiate approach to bilevel optimization problems
- Use the local Polyak-Łojasiewicz (PŁ) condition to ensure differentiability
- Choose the optimistic selection to handle non-isolated manifold lower-level solution sets
- Run experiments to evaluate the performance of the select-then-differentiate approach
- Compare the results with other optimization methods to assess its effectiveness
Who Needs to Know This
Researchers and engineers working on optimization problems, particularly those in AI and machine learning, can benefit from this approach to improve their models' performance and handle complex solution sets
Key Insight
💡 The select-then-differentiate approach can handle non-isolated manifold lower-level solution sets without requiring uniqueness of the lower-level solution
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💡 Solve bilevel optimization problems with non-isolated manifold lower-level solution sets using select-then-differentiate approach! #AI #Optimization
Key Takeaways
Learn to solve bilevel optimization problems with non-isolated manifold lower-level solution sets using the select-then-differentiate approach
Full Article
Title: Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets
Abstract:
arXiv:2605.09209v1 Announce Type: cross Abstract: 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
Abstract:
arXiv:2605.09209v1 Announce Type: cross Abstract: 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
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