How to justify the convergence of estimating the Hessian Vector Product?

[LinkToPast1990]

Hi, @HanGuo97 Do we check the convergence of estimating the hvp by empirically tracking the estimate_norm_diff? Thanks!

                pbar.update(1)
                if verbose is True:
                    new_estimate_norm = new_estimate[0].norm().item()
                    last_estimate_norm = last_estimate[0].norm().item()
                    estimate_norm_diff = new_estimate_norm - last_estimate_norm
                    pbar.set_description(f"{new_estimate_norm:.2f} | {estimate_norm_diff:.2f}")

[HanGuo97]

In principle, I think any reasonable methods would do the job (e.g., checking how the norm grows, etc). The code snippet you show tracks the growth of norm of the first element, which is just a faster, more-convenient, but likely accurate proxy.