Probabilistic Gaussian Homotopy Optimization

Probabilistic Gaussian Homotopy: A Probability-Space Continuation Framework for Nonconvex Optimization

arXiv:2603.13546v2 Announce Type: replace Abstract: We introduce Probabilistic Gaussian Homotopy (PGH), a probability-space continuation framework for nonconvex optimization. Unlike classical Gaussian homotopy, which smooths the objective and uniformly averages gradients, PGH deforms the associated Boltzmann distribution and induces Boltzmann-weighted aggregation of perturbed gradients, which exponentially biases descent directions toward low-energy regions. We show that PGH corresponds to a...