Trust-Region Optimization for Smooth Potential-Interaction Energies in Wasserstein Space

arXiv:2610.08883 · stat.ML, cs.LG, math.OC, math.PR · Submitted 2026-10-06 · Read on arXiv

stat.ML, cs.LG, math.OC, math.PR

Submitted: 2026-10-06

Updated: 2026-10-06

Comments: 24 pages, 4 figures, 1 table; code and data in the ancillary files

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Core — 10× in this paper · explained in 2 episodes
• Gradient Flow — 6× in this paper · explained in 2 episodes
• Hilbert Space — 5× in this paper · explained in 2 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Ablation — 3× in this paper · explained in 1 episode
• Trace — 2× in this paper · explained in 2 episodes
• Wasserstein Distance — 2× in this paper · explained in 5 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes

Sources

• Maximum Mean Discrepancy Gradient Flow
• Inexact JKO and proximal-gradient algorithms in the Wasserstein space
• Mirror and Preconditioned Gradient Descent in Wasserstein Space
• A Stein variational Newton method
• Information Newton's flow: second-order optimization method in probability space
• Hessian-guided Perturbed Wasserstein Gradient Flows for Escaping Saddle Points
• Wasserstein Saddle-Free Newton: Saddle Escape and Local Spectral Convergence
• Variational Analysis in the Wasserstein Space

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