Beyond backpropagation: implicit gradients for bilevel optimization

• URL: http://arxiv.org/abs/2205.03076v1
• Date: Fri, 6 May 2022 08:53:46 GMT
• Title: Beyond backpropagation: implicit gradients for bilevel optimization
• Authors: Nicolas Zucchet and Jo\~ao Sacramento
• Abstract summary: Bilevel optimization is a way to frame the learning of systems that are implicitly defined through a quantity that they minimize. Here we focus on gradient-based approaches that solve such problems. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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