Analyzing Inexact Hypgergradients for Bilevel Learning


Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modelled as the solution to an optimization problem. In this case the exact gradient with respect to the hyperparameters cannot be computed and approximate strategies are required. We provide an analysis of two classes of methods based on inexact automatic differentiation or approximate implicit differentiation. Our analysis reveals that these two strategies are actually tightly connected, and we derive a priori and a posteriori estimates for both methods which can be used to bound computations and gain further insights what their accuracy actually depends on.

1 Jun 2023
Lindon Roberts

My research is in numerical analysis, particularly nonconvex and derivative-free optimization.