Revisiting Scalable Hessian Diagonal Approximations for Applications in Reinforcement Learning

TL;DR

This paper revisits and improves a computationally efficient Hessian diagonal approximation method, HesScale, demonstrating its effectiveness in reinforcement learning and second-order optimization for small networks.

Contribution

HesScale is an improved Hessian diagonal approximation method that is computationally cheap and outperforms existing approaches in small network reinforcement learning tasks.

Findings

HesScale provides higher quality Hessian diagonal estimates than alternatives.

HesScale accelerates optimization and enhances stability in reinforcement learning.

The method shows promise for scaling to larger models in the future.

Abstract

Second-order information is valuable for many applications but challenging to compute. Several works focus on computing or approximating Hessian diagonals, but even this simplification introduces significant additional costs compared to computing a gradient. In the absence of efficient exact computation schemes for Hessian diagonals, we revisit an early approximation scheme proposed by Becker and LeCun (1989, BL89), which has a cost similar to gradients and appears to have been overlooked by the community. We introduce HesScale, an improvement over BL89, which adds negligible extra computation. On small networks, we find that this improvement is of higher quality than all alternatives, even those with theoretical guarantees, such as unbiasedness, while being much cheaper to compute. We use this insight in reinforcement learning problems where small networks are used and demonstrate HesScale in second-order optimization and scaling the step-size parameter. In our experiments, HesScale optimizes faster than existing methods and improves stability through step-size scaling. These findings are promising for scaling second-order methods in larger models in the future.