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Solving a bilevel optimization problem is at the core of several machine learning problems such as hyperparameter tuning, data denoising, meta- and few-shot learning, and training-data poisoning.
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Dimitri P Bertsekas · 1976
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A solution method for the static constrained stackelberg problem via penalty method
Eitaro Aiyoshi and Kiyotaka Shimizu · 1984
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Some properties of the bilevel programming problem
Jonathan F Bard · 1991
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Double penalty method for bilevel optimization problems
Yo Ishizuka and Eitaro Aiyoshi · 1992
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Fast exact multiplication by the hessian
Barak A Pearlmutter · 1994
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Nonlinear programming
Dimitri P Bertsekas · 1997
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Numerical optimization
Jorge Nocedal and Stephen Wright · 2006
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Imagenet: A large-scale hierarchical image database
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei · 2009
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Market structure and equilibrium
Heinrich von Stackelberg · 2010
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Is bilevel programming a special case of a mathematical program with complementarity constraints?
Stephan Dempe and Joydeep Dutta · 2012
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Generic methods for optimization-based modeling
Justin Domke · 2012
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Practical bilevel optimization: algorithms and applications , volume 30
Jonathan F Bard · 2013
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Human-level concept learning through probabilistic program induction
Brenden M Lake, Ruslan Salakhutdinov, and Joshua B Tenenbaum · 2015
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Gradient-based hyperparameter optimization through reversible learning
Dougal Maclaurin, David Duvenaud, and Ryan Adams · 2015
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Using machine teaching to identify optimal training-set attacks on machine learners
Shike Mei and Xiaojin Zhu · 2015
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Classification with noisy labels by importance reweighting
Tongliang Liu and Dacheng Tao · 2016
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Scalable gradient-based tuning of continuous regularization hyperparameters
Jelena Luketina, Mathias Berglund, Klaus Greff, and Tapani Raiko · 2016
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Hyperparameter optimization with approximate gradient
Fabian Pedregosa · 2016
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One-shot learning with memory-augmented neural networks
Adam Santoro, Sergey Bartunov, Matthew Botvinick, Daan Wierstra, and Timothy Lillicrap · 2016
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Matching networks for one shot learning
Bilevel programming for hyperparameter optimization and meta-learning
Luca Franceschi, Paolo Frasconi, Saverio Salzo, Riccardo Grazzi, and Massimiliano Pontil · 2018
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K-beam minimax: Efficient optimization for deep adversarial learning
Jihun Hamm and Yung-Kyun Noh · 2018
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Cosine normalization: Using cosine similarity instead of dot product in neural networks
Chunjie Luo, Jianfeng Zhan, Xiaohe Xue, Lei Wang, Rui Ren, and Qiang Yang · 2018
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Learning to reweight examples for robust deep learning
Mengye Ren, Wenyuan Zeng, Bin Yang, and Raquel Urtasun · 2018
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Truncated back-propagation for bilevel optimization
Amirreza Shaban, Ching-An Cheng, Nathan Hatch, and Byron Boots · 2018
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Oriol Vinyals, Charles Blundell, Tim Lillicrap, Daan Wierstra, et al · 2016
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Model-agnostic meta-learning for fast adaptation of deep networks
Chelsea Finn, Pieter Abbeel, and Sergey Levine · 2017
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Forward and reverse gradient-based hyperparameter optimization
Luca Franceschi, Michele Donini, Paolo Frasconi, and Massimiliano Pontil · 2017
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Understanding black-box predictions via influence functions
Pang Wei Koh and Percy Liang · 2017
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A simple neural attentive meta-learner
Nikhil Mishra, Mostafa Rohaninejad, Xi Chen, and Pieter Abbeel · 2017
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Towards poisoning of deep learning algorithms with back-gradient optimization
Luis Muñoz-González, Battista Biggio, Ambra Demontis, Andrea Paudice, Vasin Wongrassamee, Emil C Lupu, and Fabio Roli · 2017
Cited alongside, same era.
Optimization as a model for few-shot learning
Sachin Ravi and Hugo Larochelle · 2017
Cited alongside, same era.
Poison frogs! targeted clean-label poisoning attacks on neural networks
Ali Shafahi, W Ronny Huang, Mahyar Najibi, Octavian Suciu, Christoph Studer, Tudor Dumitras, and Tom Goldstein · 2018
Later among the works it cites.
Learning to compare: Relation network for few-shot learning
Flood Sung, Yongxin Yang, Li Zhang, Tao Xiang, Philip HS Torr, and Timothy M Hospedales · 2018
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Meta-learning with implicit gradients
Aravind Rajeswaran, Chelsea Finn, Sham M Kakade, and Sergey Levine · 2019
Closest in time.
Meta-weight-net: Learning an explicit mapping for sample weighting
Jun Shu, Qi Xie, Lixuan Yi, Qian Zhao, Sanping Zhou, Zongben Xu, and Deyu Meng · 2019
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On the iteration complexity of hypergradient computation
Riccardo Grazzi, Luca Franceschi, Massimiliano Pontil, and Saverio Salzo · 2020
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Optimizing millions of hyperparameters by implicit differentiation
Jonathan Lorraine, Paul Vicol, and David Duvenaud · 2020
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Penalty dual decomposition method for nonsmooth nonconvex optimization—part i: Algorithms and convergence analysis
Q. Shi and M. Hong · 2020
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A value-function-based interior-point method for non-convex bi-level optimization
Risheng Liu, Xuan Liu, Xiaoming Yuan, Shangzhi Zeng, and Jin Zhang · 2021
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