Learning from the Descent Direction: Adaptive Gradient Descent under One-Sided Hölder Regularity

What the math gives to ML

The paper replaces global gradient-Lipschitz control with a one-sided Hölder curvature signal measured only along the actually proposed descent direction. This is transferable as an optimizer step-size rule: estimate the positive Taylor remainder produced by a trial update, then choose the largest step justified by that directional curvature rather than by the worst variation of the full gradient. The most promising first test is a full-batch or large-batch optimizer wrapper around SGD that uses function-value probes and a sufficient-decrease safeguard, with the paper's nonconvex best-iterate rate providing a stability target.