Second-Order Optimization with Asynchronous Curvature

Second-order methods make fast progress per iteration, but forming and factorizing the Hessian often dominates their wall-clock time. We study Split-Client, a task-parallel design in which a curvature client factorizes Hessians in the background while a gradient client takes cubic-regularized steps with the most recently published matrix, so that curvature cost appears as a delay rather than as blocking time. For delayed exact Hessians, we prove a first-order stationarity bound that depends on the average age of the curvature rather than its maximum, using an overlap count and a weighted Hardy inequality that allows any bounded-error initial matrix; the analysis extends to subsampled and uniformly inexact curvature. Under a fixed-cost model, the resulting wall-clock bound matches the scaling of optimally tuned Lazy Hessian without choosing a reuse period. In experiments on two LIBSVM datasets, an implementation decreases the objective earlier in wall-clock time than Lazy and Vanilla cubic Newton, with the largest gains at intermediate accuracy.