A Single-Loop, Constant-Batch First-Order Penalty Method for Stochastic Bilevel Optimization
Recent advances in penalty-based methods for stochastic bilevel optimization (SBO) have eliminated the need for second-order derivative oracles. However, for stochastic nonconvex-strongly convex bilevel problems, existing first-order methods typically rely on nested loops and/or large batch sizes for attaining $O(ε^{-6})$ or $O(ε^{-4})$ sample complexity under standard bounded-variance assumption or mean-square smoothness assumption. Achieving these rates with a single-loop penalty method and a constant batch size remains challenging due to a large penalty value needed for an accurate approximation. To address this challenge, we develop a stochastic SIngle-loop COnstant-Batch first-order ...
| Authors | Xingyu Chen, Ming Yang, Quanqi Hu et al. |
|---|---|
| Primary category | math.OC |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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