Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions

TL;DR

Self-Tuning Networks (STNs) introduce a scalable bilevel optimization approach that adaptively tunes hyperparameters during training by approximating the best-response function, outperforming existing methods on large-scale deep learning tasks.

Contribution

The paper presents a novel method for online hyperparameter tuning using structured best-response approximations, enabling adaptive and discrete hyperparameter optimization without differentiating the training loss.

Findings

Outperforms existing hyperparameter optimization methods on large-scale problems

Allows tuning of discrete hyperparameters, data augmentation, and dropout probabilities

Discovers hyperparameter schedules that outperform fixed values

Abstract

Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact best-response for a shallow linear network with L2-regularized Jacobian can be represented by a similar gating mechanism. We fit this model using a gradient-based hyperparameter optimization algorithm which alternates between approximating the best-response around the current hyperparameters and optimizing the hyperparameters using the approximate best-response function. Unlike other gradient-based approaches, we do not require differentiating the training loss with respect to the hyperparameters, allowing us to tune discrete hyperparameters, data augmentation hyperparameters, and dropout probabilities. Because the hyperparameters are adapted online, our approach discovers hyperparameter schedules that can outperform fixed hyperparameter values. Empirically, our approach outperforms competing hyperparameter optimization methods on large-scale deep learning problems. We call our networks, which update their own hyperparameters online during training, Self-Tuning Networks (STNs).