Probabilistic Gaussian Homotopy: A Probability-Space Continuation Framework for Nonconvex Optimization
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 log-sum-exp (soft-min) homotopy that smooths a nonconvex objective at scale $λ>0$ and recovers the original objective as $λ\to 0$, yielding a posterior-mean generalization of the Moreau envelope, and we derive a dynamical system governing minimizer evo...
| Authors | Eshed Gal, Samy Wu Fung, Eldad Haber |
|---|---|
| Primary category | cs.LG |
| Published | 13 March 2026 |
| Last updated at source | 4 June 2026 |
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