Particle-based Generalised Stochastic Optimisation

2026/08/03 by Jiechen Jackie Zhang, O. Deniz Akyildiz
Mathematics · Computer Science · #stat.ML #cs.LG #stat.CO

paper · pdf

arxiv created 2026/08/03 · arxiv updated 2026/08/05

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.

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