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Learning with Differentiable Pertubed Optimizers
Quentin Berthet · Mathieu Blondel · Olivier Teboul · Marco Cuturi · Jean-Philippe Vert · Francis Bach

Thu Dec 10 09:00 AM -- 11:00 AM (PST) @ Poster Session 5 #1489

Machine learning pipelines often rely on optimizers procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed in a forward manner, 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 optimizers into operations that are differentiable and never locally constant. Our approach relies on stochastically perturbed optimizers, and can be used readily within existing solvers. Their derivatives can be evaluated efficiently, and smoothness tuned via the chosen noise amplitude. We also show how this framework can be connected to a family of losses developed in structured prediction, and give theoretical guarantees for their use in learning tasks. We demonstrate experimentally the performance of our approach on various tasks.

Author Information

Quentin Berthet (Google Brain)
Mathieu Blondel (Google)
Olivier Teboul (Ecole Centrale Paris)
Marco Cuturi (Google Brain & CREST - ENSAE)

Marco Cuturi is a research scientist at Google AI, Brain team in Paris. He received his Ph.D. in 11/2005 from the Ecole des Mines de Paris in applied mathematics. Before that he graduated from National School of Statistics (ENSAE) with a master degree (MVA) from ENS Cachan. He worked as a post-doctoral researcher at the Institute of Statistical Mathematics, Tokyo, between 11/2005 and 3/2007 and then in the financial industry between 4/2007 and 9/2008. After working at the ORFE department of Princeton University as a lecturer between 2/2009 and 8/2010, he was at the Graduate School of Informatics of Kyoto University between 9/2010 and 9/2016 as a tenured associate professor. He joined ENSAE in 9/2016 as a professor, where he is now working part-time. His main employment is now with Google AI (Brain team in Paris) since 10/2018, as a research scientist working on fundamental aspects of machine learning.

Jean-Philippe Vert (Google)
Francis Bach (INRIA - Ecole Normale Superieure)

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