Bilevel Programming for Hyperparameter Optimization and Meta-Learning

TL;DR

This paper proposes a bilevel programming framework that unifies hyperparameter optimization and meta-learning, providing theoretical convergence guarantees and demonstrating effectiveness in deep learning and few-shot learning scenarios.

Contribution

It introduces an approximate bilevel optimization method that accounts for optimization dynamics, unifying hyperparameter tuning and meta-learning with theoretical convergence analysis.

Findings

The approach converges to solutions of the exact bilevel problem.

Encouraging results in few-shot learning experiments.

Outperforms classical learning-to-learn methods.

Abstract

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.