Finite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows

Key points

• Its Hessian-guided perturbed variant (PWGF) adds Gaussian perturbations to escape saddle points in nonconvex problems.1
• Our analysis retains the curvature accumulated along the population-driven reference path: negative curvature can amplify approximation errors, while subsequent positive curvature can damp their influence.1
• Under regularity assumptions and a prescribed common perturbation schedule, we prove particle and objective-value tracking bounds on a high-probability event for reference paths satisfying explicit conditions on accumulated curvature.1
• To handle state-dependent Gaussian jumps, we construct a population-first coupling that preserves the reference particles' conditional independence and reduces jump errors to covariance comparison.1

Sources (1)

• [1]Finite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 03:13 PM

  Wasserstein gradient flow extends gradient descent to probability measures.

  Its Hessian-guided perturbed variant (PWGF) adds Gaussian perturbations to escape saddle points in nonconvex problems.

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