Particle-based Generalised Stochastic Optimisation
stat.ML, cs.LG, stat.CO
Submitted: 2026-08-03
Updated: 2026-10-09
License: http://creativecommons.org/licenses/by/4.0/
The gist: We develop a class of diffusion-based stochastic particle optimisation methods for loss functions with intractable gradients.
Terminology
Abstract
We develop a class of diffusion-based stochastic particle optimisation methods for loss functions with intractable gradients. Specifically, we consider problems in which the loss gradient is an integral with respect to a parameter-dependent distribution, a structure that includes training generative models, fine-tuning, and learning latent-variable models. We introduce mean-field dynamics and its interacting-particle approximations, which contain several existing algorithms as special cases and provides a route to constructing new methods. Under well-posedness and joint contractivity assumptions, we prove exponential convergence and show that the continuous-time particle system admits a non-asymptotic error bound. We illustrate it by developing momentum and higher-order Langevin variants and evaluating them on maximum marginal-likelihood estimation and energy-based-model training.
Sources
- A Unifying and Canonical Description of Measure-Preserving Diffusions
- Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations
- Kinetic Interacting Particle Langevin Monte Carlo
- Uniform-in-time convergence bounds for Persistent Contrastive Divergence algorithms
- How to Train Your Energy-Based Models
- Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis
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