Beyond backpropagation: bilevel optimization through implicit differentiation and equilibrium propagation

Abstract

This paper reviews gradient-based techniques to solve bilevel optimization problems. Bilevel optimization is a general way to frame the learning of systems that are implicitly defined through a quantity that they minimize. This characterization can be applied to neural networks, optimizers, algorithmic solvers and even physical systems, and allows for greater modeling flexibility compared to an explicit definition of such systems. Here we focus on gradient-based approaches that solve such problems. We distinguish them in two categories: those rooted in implicit differentiation, and those that leverage the equilibrium propagation theorem. We present the mathematical foundations that are behind such methods, introduce the gradient-estimation algorithms in detail and compare the competitive advantages of the different approaches.

References in corpus (9)

• TensorFlow: A system for large-scale machine learning
• Theoretical Models of Learning to Learn
• Hybrid Deterministic-Stochastic Methods for Data Fitting
• Stochastic Hyperparameter Optimization through Hypernetworks
• Supervised learning in physical networks: From machine learning to learning machines
• A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic
• Training End-to-End Analog Neural Networks with Equilibrium Propagation
• A deep learning theory for neural networks grounded in physics
• Agnostic Physics-Driven Deep Learning

Cited by in corpus (1)

• An adaptively inexact first-order method for bilevel optimization with application to hyperparameter learning