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Bilevel optimization has arisen as a powerful tool for many machine learning problems such as meta-learning, hyperparameter optimization, and reinforcement learning.
Mathematical programs with optimization problems in the constraints
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New branch-and-bound rules for linear bilevel programming
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Gradient-based learning applied to document recognition
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Actor-critic algorithms
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Multi-step model-agnostic meta-learning: Convergence and improved algorithms
Ji, K., Yang, J., and Liang, Y · 2002
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An extended kuhn–tucker approach for linear bilevel programming
Shi, C., Lu, J., and Zhang, G · 2005
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Classification model selection via bilevel programming
Kunapuli, G., Bennett, K. P., Hu, J., and Pang, J.-S · 2008
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Learning multiple layers of features from tiny images
Krizhevsky, A. and Hinton, G · 2009
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Bilevel programming algorithms for machine learning model selection
Moore, G. M · 2010
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Generic methods for optimization-based modeling
Domke, J · 2012
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Learning constrained task similarities in graphregularized multi-task learning
Flamary, R., Rakotomamonjy, A., and Gasso, G · 2014
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Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J · 2014
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Gradient-based hyperparameter optimization through reversible learning
Maclaurin, D., Duvenaud, D., and Adams, R · 2015
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Imagenet large scale visual recognition challenge
Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., Berg, A. C., and Fei-Fei, L · 2015
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Gould, S., Fernando, B., Cherian, A., Anderson, P., Cruz, R. S., and Guo, E · 2016
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Hyperparameter optimization with approximate gradient
Pedregosa, F · 2016
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Watch and learn: Optimizing from revealed preferences feedback
Roth, A., Ullman, J., and Wu, Z. S · 2016
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Matching networks for one shot learning
Vinyals, O., Blundell, C., Lillicrap, T., and Wierstra, D · 2016
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Model-agnostic meta-learning for fast adaptation of deep networks
Finn, C., Abbeel, P., and Levine, S · 2017
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Forward and reverse gradient-based hyperparameter optimization
Franceschi, L., Donini, M., Frasconi, P., and Pontil, M · 2017
learn2learn , 2019
Arnold, S. M., Mahajan, P., Datta, D., and Bunner, I · 2019
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Hyperparameter optimization
Feurer, M. and Hutter, F · 2019
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Rapid learning or feature reuse? towards understanding the effectiveness of MAML
Raghu, A., Raghu, M., Bengio, S., and Vinyals, O · 2019
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Meta-learning with implicit gradients
Rajeswaran, A., Finn, C., Kakade, S. M., and Levine, S · 2019
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Truncated back-propagation for bilevel optimization
Shaban, A., Cheng, C.-A., Hatch, N., and Boots, B · 2019
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Adversarial attacks on graph neural networks via meta learning
Zügner, D. and Günnemann, S · 2019
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Prototypical networks for few-shot learning
Snell, J., Swersky, K., and Zemel, R · 2017
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Meta-learning with differentiable closed-form solvers
Bertinetto, L., Henriques, J. F., Torr, P., and Vedaldi, A · 2018
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Bilevel programming for hyperparameter optimization and meta-learning
Franceschi, L., Frasconi, P., Salzo, S., Grazzi, R., and Pontil, M · 2018
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Approximation methods for bilevel programming
Ghadimi, S. and Wang, M · 2018
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Reviving and improving recurrent back-propagation
Liao, R., Xiong, Y., Fetaya, E., Zhang, L., Yoon, K., Pitkow, X., Urtasun, R., and Zemel, R · 2018
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Hyperparameter learning via bilevel nonsmooth optimization
Okuno, T., Takeda, A., and Kawana, A · 2018
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On the iteration complexity of hypergradient computation
Grazzi, R., Franceschi, L., Pontil, M., and Salzo, S · 2020
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Hong, M., Wai, H.-T., Wang, Z., and Yang, Z · 2020
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Improved bilevel model: Fast and optimal algorithm with theoretical guarantee
Li, J., Gu, B., and Huang, H · 2020
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A generic first-order algorithmic framework for bi-level programming beyond lower-level singleton
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Optimizing millions of hyperparameters by implicit differentiation
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Hyper-parameter optimization: A review of algorithms and applications
Yu, T. and Zhu, H · 2020
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Lower bounds and accelerated algorithms for bilevel optimization
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