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Bilevel optimization is a popular two-level hierarchical optimization, which has been widely applied to many machine learning tasks such as hyperparameter learning, meta learning and continual learning.
Gradient methods for the minimisation of functionals
Boris Polyak · 1963
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Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator
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Bilevel programming for hyperparameter optimization and meta-learning
Luca Franceschi, Paolo Frasconi, Saverio Salzo, Riccardo Grazzi, and Massimiliano Pontil · 2018
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Lectures on convex optimization , volume 137
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Zhe Wang, Kaiyi Ji, Yi Zhou, Yingbin Liang, and Vahid Tarokh · 2019
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Mingyi Hong, Hoi-To Wai, Zhaoran Wang, and Zhuoran Yang · 2020
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Ufo-blo: Unbiased first-order bilevel optimization
Valerii Likhosherstov, Xingyou Song, Krzysztof Choromanski, Jared Davis, and Adrian Weller · 2020
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A generic first-order algorithmic framework for bi-level programming beyond lower-level singleton
Risheng Liu, Pan Mu, Xiaoming Yuan, Shangzhi Zeng, and Jin Zhang · 2020
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Closing the gap: Tighter analysis of alternating stochastic gradient methods for bilevel problems
Tianyi Chen, Yuejiao Sun, and Wotao Yin · 2021
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Proxy convexity: A unified framework for the analysis of neural networks trained by gradient descent
Spencer Frei and Quanquan Gu · 2021
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On stochastic moving-average estimators for non-convex optimization
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Feihu Huang, Junyi Ji, and Shangqian Gao · 2021
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Will bilevel optimizers benefit from loops
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Bome! bilevel optimization made easy: A simple first-order approach
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A constrained optimization approach to bilevel optimization with multiple inner minima
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