Learning from the Descent Direction: Adaptive Gradient Descent under One-Sided H\"older Regularity

תקציר מקורי באנגליתarXiv:2607.22906v1 Announce Type: new Abstract: We study adaptive gradient descent for continuously differentiable, possibly nonconvex objectives under one-sided H\"older regularity. Unlike classical H\"older- or Lipschitz-gradient assumptions, which control the full gradient variation, our condition bounds only the directional term appearing in the descent inequality. This can allow less conservative step sizes when large gradient changes are orthogonal to, or favorable along, the update direction. We propose an adaptive scalar-step method based on an estimate of positive one-sided H\"older curvature, combined with a simple sufficient-decrease safeguard. For nonconvex objectives on a convex region containing the accepted update segments, we prove an explicit best-iterate stationarity boun