## Provably Faster Algorithms for Bilevel Optimization

May 21, 2021 (edited Jan 21, 2022)NeurIPS 2021 SpotlightReaders: Everyone
• Keywords: Bilevel Optimization, Momentum, Recursive Gradient Estimator, Hessian Vector Computation
• TL;DR: This paper proposes two bilevel optimizers that provably outperform all existing algorithms by the order of magnitude.
• Abstract: 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 $\mathcal{\widetilde O}(\epsilon^{-2})$ 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 $\mathcal{\widetilde O}(\epsilon^{-1.5})$, 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.
• Supplementary Material: pdf
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• Code: https://github.com/JunjieYang97/MRVRBO
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