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This research introduces diffusion-based stochastic particle optimization methods designed specifically for loss functions where gradients are intractable, addressing key challenges in training generative models and latent-variable systems. By establishing exponential convergence under mean-field dynamics, the work provides a rigorous theoretical foundation that generalizes existing algorithms like Langevin variants while offering new non-asymptotic error bounds. These advancements directly impact the scalability and reliability of complex machine learning architectures where traditional gradient-based approaches fail.
Particle-based Generalised Stochastic Optimisation
arXiv:2608.02844v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG); Computation (stat.CO)
arXiv:2608.02844 [stat.ML]
(or arXiv:2608.02844v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2608.02844 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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