Towards Understanding Gradient Approximation in Equality Constrained Deep Declarative Networks

Stephen Gould, Ming Xu, Zhiwei Xu, Yanbin Liu

Keywords: Deep Declarative Networks, Differentiable Optimization, Gradient Approximation

TL;DR: We explore conditions for when gradient approximation results in a descent direction for differentiating through optimization problems.

Abstract: We explore conditions for when the gradient of a deep declarative node can be approximated by ignoring constraint terms and still result in a descent direction for the global loss function. This has important practical application when training deep learning models since the approximation is often computationally much more efficient than the true gradient calculation. We provide theoretical analysis for problems with linear equality constraints and normalization constraints, and show examples where the approximation works well in practice as well as some cautionary tales for when it fails.

Submission Number: 2