Papers › Provably Faster Algorithms for Bilevel Optimization

Provably Faster Algorithms for Bilevel Optimization

8 Jun 2021NeurIPS 2021 12arXiv:2106.04692archive 2025-07-28

Junjie Yang, Kaiyi Ji, Yingbin Liang

Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization problems faster. However, those momentum-based algorithms do not achieve provably better computational complexity than 𝒪(ϵ⁻²) of the SGD-based algorithm. In this paper, we propose two new algorithms for bilevel optimization, where the first algorithm adopts momentum-based recursive iterations, and the second algorithm adopts recursive gradient estimations in nested loops to decrease the variance. We show that both algorithms achieve the complexity of 𝒪(ϵ^(-1.5)), which outperforms all existing algorithms by the order of magnitude. Our experiments validate our theoretical results and demonstrate the superior empirical performance of our algorithms in hyperparameter applications.

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