Learning to Learn with Smooth Regularization

Yuanhao Xiong, Cho-Jui Hsieh ;

"Recent decades have witnessed great advances of deep learning in tackling various problems such as classification and decision making. The rapid development gave rise to a novel framework, Learning-to-Learn (L2L), in which an automatic optimization algorithm (optimizer) modeled by neural networks is expected to learn rules for updating the target objective function (optimizee). Despite its advantages for specific problems, L2L still cannot replace classic methods due to its instability. Unlike hand-engineered algorithms, neural optimizers may suffer from the instability issue---under distinct but similar states, the same neural optimizer can produce quite different updates. Motivated by the stability property that should be satisfied by an ideal optimizer, we propose a regularization term that can enforce the smoothness and stability of the learned optimizers. Comprehensive experiments on the neural network training tasks demonstrate that the proposed regularization consistently improve the learned neural optimizers even when transferring to tasks with different architectures and datasets. Furthermore, we show that our smoothness-inducing regularizer can improve the performance of neural optimizers on few-shot learning tasks. Code can be found at https://github.com/xyh97/SmoothedOptimizer."