A Bilevel Optimization Approach for Parameter Learning in Variational Models

By Karl Kunisch, Thomas Pock. 2013

233 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Hyperparameter optimization with approximate gradient (2016, methodology): “This is the iterative differentiation approach from (Domke, 2012), using the same inner-optimization algorithm as H OAG .”
OptNet: Differentiable Optimization as a Layer in Neural Networks (2017, neutral): “These techniques also come up in bilevel optimization (Gould et al., 2016; Kunisch & Pock, 2013) and sensitivity analysis (Bertsekas, 1999; Fiacco & Ishizuka, 1990; Bonnans & Shapiro, 2013).”
Structured Prediction Energy Networks (2015, neutral): “Alter-natively, non-iterative feed-forward predictors can be constructed using structured models as motivation (Stoyanov et al., 2011; Domke, 2013; Kunisch & Pock, 2013; Her-shey et al., 2014; Li & Zemel, 2014; Zheng et al., 2015).”
Bilevel approaches for learning of variational imaging models (2015, methodology): “…that – based on a more or less generic model setup such as (1) – aim to optimise operators (i.e., matrices and expansion) and functions (i.e. distance functions d ) in a functional variational regularisation approach by bilevel learning from ‘examples’ [46, 31, 54, 4, 74, 24, 33, 32], among others.”
The structure of optimal parameters for image restoration problems (2015, methodology): “Recently parameter learning in the context of functional variational regularisation models also entered the image processing community with works by the authors [23,14], Kunisch, Pock and co-workers [37,17] and Chung et al.”
Modern regularization methods for inverse problems (2018, background): “If uj ∈ R(f δ j ,α) stems from an optimization problem, then (103) is also known as a bilevel optimization problem [254, 321].”
Learning End-to-end Video Classification with Rank-Pooling (2016, background): “It has recently gained interest in the machine learning community in the context of hyperparameter learning (Klatzer & Pock, 2015; Do et al., 2007) and in the computer vision community in the context of image denoising (Domke, 2012; Kunisch & Pock, 2013).”
Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions (2019, methodology): “Similar approaches have been used for hyperparameter optimization in log-linear models (Foo et al., 2008), kernel selection (Chapelle et al., 2002; Seeger, 2007), and image reconstruction (Kunisch & Pock, 2013; Calatroni et al., 2015).”
Techniques for Gradient-Based Bilevel Optimization with Non-smooth Lower Level Problems (2016, methodology): “The problem where ρ(x) = |x| is considered in [22,9], however only a smooth approximation is solved in the end.”
Bilevel Optimization with Nonsmooth Lower Level Problems (2015, methodology): “We consider a bilevel optimization problem for parameter learning of the form as considered in [1, 2].”