Stochastic Nonconvex Bilevel Optimization: Improved Rates Without Rare-Visit Assumption
We investigate stochastic simple bilevel optimization with smooth and possibly nonconvex upper- and lower-level objectives. Existing stochastic extensions of dynamic barrier gradient descent (DBGD) either obtain fast convergence under an unverifiable trajectory-dependent ``rare-visit'' assumption, or remove this assumption at a substantially higher oracle cost. We show that a simple denominator-only regularization of the DBGD multiplier eliminates the need for such an assumption while preserving fast convergence rates. Specifically, our method achieves $(\varepsilon, \varepsilon)$-stationarity in $O(\varepsilon^{-2})$ iterations using $O(\varepsilon^{-4})$ upper-level and $O(\varepsilon^{...
| Authors | Daniel Cortild, Mathias Staudigl, Juan Peypouquet et al. |
|---|---|
| Primary category | math.OC |
| Published | 6 September 2026 |
| Last updated at source | 6 September 2026 |
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