Optimizing Millions of Hyperparameters by Implicit Differentiation
This enables scalable hyperparameter tuning for large-scale models, though it is incremental as it builds on existing implicit differentiation methods.
The paper tackles the problem of efficiently optimizing millions of hyperparameters in neural networks by proposing an algorithm based on implicit differentiation and inverse Hessian approximations, achieving this with only a few times more memory and compute than standard training.
We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.