Revisiting Scalable Hessian Diagonal Approximations for Applications in Reinforcement Learning
This work addresses the problem of efficient second-order optimization for researchers and practitioners in reinforcement learning, though it is incremental as it builds on an existing approximation scheme.
The authors tackled the computational challenge of approximating Hessian diagonals in second-order optimization by revisiting and improving an overlooked early scheme, resulting in HesScale, which offers higher quality approximations than alternatives on small networks with negligible extra cost and demonstrates faster optimization and improved stability in reinforcement learning applications.
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.