  Being the most classical generative model for serial data, state-space models
(SSM) are fundamental in AI and statistical machine learning. In SSM, any form
of parameter learning or latent state inference typically involves the
computation of complex latent-state posteriors. In this work, we build upon the
variational sequential Monte Carlo (VSMC) method, which provides
computationally efficient and accurate model parameter estimation and Bayesian
latent-state inference by combining particle methods and variational inference.
While standard VSMC operates in the offline mode, by re-processing repeatedly a
given batch of data, we distribute the approximation of the gradient of the
VSMC surrogate ELBO in time using stochastic approximation, allowing for online
learning in the presence of streams of data. This results in an algorithm,
online VSMC, that is capable of performing efficiently, entirely on-the-fly,
both parameter estimation and particle proposal adaptation. In addition, we
provide rigorous theoretical results describing the algorithm's convergence
properties as the number of data tends to infinity as well as numerical
illustrations of its excellent convergence properties and usefulness also in
batch-processing settings.
