Bilevel Programming for Hyperparameter Optimization and Meta-Learning
This work addresses the challenge of efficiently optimizing hyperparameters and meta-learners in machine learning, though it appears incremental as it builds on existing bilevel programming concepts.
The paper tackles the problem of unifying gradient-based hyperparameter optimization and meta-learning by introducing a bilevel programming framework, showing that approximate solutions converge to exact ones under certain conditions and achieving encouraging results in few-shot learning experiments.
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.