Newton-Based Methods for Bilevel Optimization Beyond Lower-Level Strong Convexity
Bilevel optimization provides a framework for machine learning tasks such as hyperparameter optimization, data reweighting, and meta-learning. Existing Newton-based bilevel methods typically rely on the classical hypergradient formula, which is generally unavailable when lower-level solutions are nonunique and the lower-level Hessian is singular. We develop two Newton-based methods beyond lower-level strong convexity by exploiting curvature shared by the lower-level and multiplier updates. Newton-based GALET handles potentially singular lower-level curvature under a positive spectral-gap condition, exploiting its range structure to avoid the squared-Hessian multiplier system used in GALET...
| Authors | Youran Dong, Junfeng Yang, Wei Yao et al. |
|---|---|
| Primary category | math.OC |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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