To Solve Bilevel Optimization with Nonconvex Lower Levels, We Need Second-Order Stationarity
Although bilevel optimization (BLO) has emerged as a powerful framework for addressing many complex and nested machine learning problems in recent years, most existing studies are confined to the lower-level strongly convex (LLSC) or lower-level generally convex (LLGC) settings (i.e., the lower-level objective function is assumed to be, at least, convex). While the LLSC/LLGC assumptions render more tractable algorithmic design and theoretical analysis, they are too rigid to encompass many machine learning problems in practice. The limitations of LLSC/LLGC assumptions in BLO motivate us to investigate solving the BLO problem in the general lower-level nonconvex (LLNC) settings, which remai...
| Authors | Zhiyao Zhang, Menglu Yu, Alvaro Velasquez et al. |
|---|---|
| Primary category | cs.LG |
| Published | 24 September 2026 |
| Last updated at source | 24 September 2026 |
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