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Bilevel Programming for Hyperparameter Optimization and Meta-Learning
Luca Franceschi · Paolo Frasconi · Saverio Salzo · Riccardo Grazzi · Massimiliano Pontil

Wed Jul 11 02:40 AM -- 02:50 AM (PDT) @ A3

We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the optimization dynamics for the inner objective. Depending on the specific setting, the outer variables take either the meaning of hyperparameters in a supervised learning problem or parameters of a meta-learner.We provide sufficient conditions under which solutions of the approximate problem converge to those of the exact problem. We instantiate our approach for meta-learning in the case of deep learning where representation layers are treated as hyperparameters shared across a set of training episodes. In experiments, we confirm our theoretical findings, present encouraging results for few-shot learning and contrast the bilevel approach against classical approaches for learning-to-learn.

Author Information

Luca Franceschi (Istituto Italiano di Tecnologia - University College London)
Paolo Frasconi (University of Florence)
Saverio Salzo (Istituto Italiano di Tecnologia)
Riccardo Grazzi (Istituto Italiano di Tecnologia)
Massimiliano Pontil (University College London)

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