Français
Learning with differentiable perturbed optimizers
Post-edited
Authors : Berthet, Quentin (Author of the conference)
CIRM (Publisher )
62F99 - None of the above but in this section
68W20 - randomized algorithms
90C06 - Large-scale problems
Additional resources :
https://www.cirm-math.fr/RepOrga/2133/Slides/perturbations_berthet.pdf
CIRM (Publisher )
Abstract :
Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g. sorting, picking closest neighbors, finding shortest paths or optimal matchings). Although these discrete decisions are easily computed in a forward manner, they cannot be used to modify model parameters using first-order optimization techniques because they break the back-propagation of computational graphs. In order to expand the scope of learning problems that can be solved in an end-to-end fashion, we propose a systematic method to transform a block that outputs an optimal discrete decision into a differentiable operation. Our approach relies on stochastic perturbations of these parameters, and can be used readily within existing solvers without the need for ad hoc regularization or smoothing. These perturbed optimizers yield solutions that are differentiable and never locally constant. The amount of smoothness can be tuned via the chosen noise amplitude, whose impact we analyze. The derivatives of these perturbed solvers can be evaluated eciently. We also show how this framework can be connected to a family of losses developed in structured prediction, and describe how these can be used in unsupervised and supervised learning, with theoretical guarantees.
We demonstrate the performance of our approach on several machine learning tasks in experiments on synthetic and real data.
Keywords : perturbation methods; structured learning
MSC Codes : We demonstrate the performance of our approach on several machine learning tasks in experiments on synthetic and real data.
Keywords : perturbation methods; structured learning
62F99 - None of the above but in this section
68W20 - randomized algorithms
90C06 - Large-scale problems
Additional resources :
https://www.cirm-math.fr/RepOrga/2133/Slides/perturbations_berthet.pdf
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 06/04/2020 Conference Date : 09/03/2020 Subseries : Research talks arXiv category : Machine Learning ; Optimization and Control Mathematical Area(s) : Computer Science ; Control Theory & Optimization Format : MP4 (.mp4) - HD Video Time : 00:50:11 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/20120-03-09_Berthet.mp4 
|
Information on the Event
Event Title : Optimization for Machine Learning / Optimisation pour l'apprentissage automatiqueEvent Organizers : Boyer, Claire ; d'Aspremont, Alexandre ; Gramfort, Alexandre ; Salmon, Joseph ; Villar, Soledad Dates : 09/03/2020 - 13/03/2020 Event Year : 2020 Event URL : https://conferences.cirm-math.fr/2133.html
Citation Data
DOI : 10.24350/CIRM.V.19622903Cite this video as: Berthet, Quentin (2020). Learning with differentiable perturbed optimizers. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19622903 URI : http://dx.doi.org/10.24350/CIRM.V.19622903 |
See Also
- [Multi angle] Rank optimality for the Burer-Monteiro factorization / Author of the conference Waldspurger, Irène.
- [Multi angle] What does back propagation compute? / Author of the conference Pauwels, Edouard.
- [Multi angle] Bridging the gap between optimal transport and MMD Sinkhorn divergences / Author of the conference Genevay, Aude.
- [Multi angle] Gradient descent for wide two-layer neural networks / Author of the conference Bach, Francis.
Bibliography
- PAPANDREOU, George et YUILLE, Alan L. Perturb-and-map random fields: Using discrete optimization to learn and sample from energy models. In : 2011 International Conference on Computer Vision. IEEE, 2011. p. 193-200. - https://doi.org/10.1109/ICCV.2011.6126242
- KALAI, Adam et VEMPALA, Santosh. Efficient algorithms for online decision problems. In : Learning Theory and Kernel Machines. Springer, Berlin, Heidelberg, 2003. p. 26-40. - http://dx.doi.org/10.1007/978-3-540-45167-9_4
- BERTHET, Quentin, BLONDEL, Mathieu, TEBOUL, Olivier, et al. Learning with Differentiable Perturbed Optimizers. arXiv preprint arXiv:2002.08676, 2020. - https://arxiv.org/abs/2002.08676
