  The learning rate (LR) is one of the most important hyper-parameters in
stochastic gradient descent (SGD) algorithm for training deep neural networks
(DNN). However, current hand-designed LR schedules need to manually pre-specify
a fixed form, which limits their ability to adapt practical non-convex
optimization problems due to the significant diversification of training
dynamics. Meanwhile, it always needs to search proper LR schedules from scratch
for new tasks, which, however, are often largely different with task
variations, like data modalities, network architectures, or training data
capacities. To address this learning-rate-schedule setting issues, we propose
to parameterize LR schedules with an explicit mapping formulation, called
\textit{MLR-SNet}. The learnable parameterized structure brings more
flexibility for MLR-SNet to learn a proper LR schedule to comply with the
training dynamics of DNN. Image and text classification benchmark experiments
substantiate the capability of our method for achieving proper LR schedules.
Moreover, the explicit parameterized structure makes the meta-learned LR
schedules capable of being transferable and plug-and-play, which can be easily
generalized to new heterogeneous tasks. We transfer our meta-learned MLR-SNet
to query tasks like different training epochs, network architectures, data
modalities, dataset sizes from the training ones, and achieve comparable or
even better performance compared with hand-designed LR schedules specifically
designed for the query tasks. The robustness of MLR-SNet is also substantiated
when the training data are biased with corrupted noise. We further prove the
convergence of the SGD algorithm equipped with LR schedule produced by our
MLR-Net, with the convergence rate comparable to the best-known ones of the
algorithm for solving the problem.
