One-step differentiation of iterative algorithms
Keywords: automatic differentiation, implicit differentiation, super-linear algorithms, bilevel optimization.
TL;DR: One-step differentiation is as easy as autodiff, and as performant as implicit differentiation.
Abstract: In appropriate frameworks, automatic differentiation is transparent to the user, at the cost of being a significant computational burden when the number of operations is large. For iterative algorithms, implicit differentiation alleviates this issue but requires custom implementation of Jacobian evaluation. In this paper, we study one-step differentiation, also known as Jacobian-free backpropagation, a method as easy as automatic differentiation and as performant as implicit differentiation for fast algorithms (e.g. superlinear optimization methods). We provide a complete theoretical approximation analysis with specific examples (Newton's method, gradient descent) along with its consequences in bilevel optimization. Several numerical examples illustrate the well-foundness of the one-step estimator.
Submission Number: 1846
Loading