Preconditioned sharpness analysis for DH-KFAC in deep hedging

Establish a precise analysis, using the preconditioned sharpness framework, of the optimization dynamics when training deep hedging policies with the DH-KFAC generalized Gauss–Newton preconditioner, quantifying curvature properties of the deep hedging loss surface along the optimization trajectory and clarifying the method’s behavior in high-curvature regions.

Background

In the experiments, the authors observe that DH-KFAC progresses faster per iteration than Adam and appears to enter regions of the loss surface with higher curvature, as suggested by increasing largest eigenvalues of the preconditioner and higher gradient variance encountered along the optimization path.

To rigorously understand these observations, the authors point to the need for a formal analysis using the preconditioned sharpness framework, which assesses training stability and convergence in high-curvature regimes by accounting for the optimizer’s preconditioning effects.