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Bilevel optimization has found extensive applications in modern machine learning problems such as hyperparameter optimization, neural architecture search, meta-learning, etc.
The fritz john necessary optimality conditions in the presence of equality and inequality constraints
Olvi L Mangasarian and Stan Fromovitz · 1967
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Actor-critic algorithms
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Generic methods for optimization-based modeling
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Stephen Gould, Basura Fernando, Anoop Cherian, Peter Anderson, Rodrigo Santa Cruz, and Edison Guo · 2016
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Hyperparameter optimization with approximate gradient
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Meta-learning with differentiable closed-form solvers
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Bilevel programming for hyperparameter optimization and meta-learning
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Reviving and improving recurrent back-propagation
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Darts: Differentiable architecture search
Hanxiao Liu, Karen Simonyan, and Yiming Yang · 2018
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Lectures on convex optimization , volume 137
Yurii Nesterov et al · 2018
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Stochastic first-order methods for convex and nonconvex functional constrained optimization
Digvijay Boob, Qi Deng, and Guanghui Lan · 2019
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Matthew MacKay, Paul Vicol, Jon Lorraine, David Duvenaud, and Roger Grosse · 2019
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Improved bilevel model: Fast and optimal algorithm with theoretical guarantee
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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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Optimizing millions of hyperparameters by implicit differentiation
Jonathan Lorraine, Paul Vicol, and David Duvenaud · 2020
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Proximally constrained methods for weakly convex optimization with weakly convex constraints
Runchao Ma, Qihang Lin, and Tianbao Yang · 2020
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A single-timescale stochastic bilevel optimization method
Tianyi Chen, Yuejiao Sun, and Wotao Yin · 2021
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Meta-learning with implicit gradients
Aravind Rajeswaran, Chelsea Finn, Sham M Kakade, and Sergey Levine · 2019
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Truncated back-propagation for bilevel optimization
Amirreza Shaban, Ching-An Cheng, Nathan Hatch, and Byron Boots · 2019
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Bilevel optimization
Stephan Dempe and Alain Zemkoho · 2020
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Mingyi Hong, Hoi-To Wai, Zhaoran Wang, and Zhuoran Yang · 2020
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Convergence of meta-learning with task-specific adaptation over partial parameter
Kaiyi Ji, Jason D Lee, Yingbin Liang, and H Vincent Poor · 2020
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First-order and Stochastic Optimization Methods for Machine Learning
Guanghui Lan · 2020
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On the iteration complexity of hypergradient computation
Riccardo Grazzi, Luca Franceschi, Massimiliano Pontil, and Saverio Salzo
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Randomized stochastic variance-reduced methods for stochastic bilevel optimization
Zhishuai Guo and Tianbao Yang · 2021
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Lower bounds and accelerated algorithms for bilevel optimization
Kaiyi Ji and Yingbin Liang · 2021
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Bilevel optimization: Convergence analysis and enhanced design
Kayi Ji, Junjie Yang, and Yingbin Liang · 2021
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A near-optimal algorithm for stochastic bilevel optimization via double-momentum
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Provably faster algorithms for bilevel optimization
Junjie Yang, Kaiyi Ji, and Yingbin Liang · 2021
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