Title: Learning to Learn with Smooth Regularization. Abstract: Recent decades have witnessed great prosperity of deep learning in tackling various problems such as classification and decision making. The rapid development stimulates 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---when provided with similar states (a combination of some metrics to describe the optimizee), 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 neural 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 data. Furthermore, we show that our regularizer can improve the performance of neural optimizers on few-shot learning tasks. 