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.

翻译：作为处理序列数据的最经典生成模型，状态空间模型（SSM）是人工智能与统计机器学习领域的基础模型。在SSM中，任何形式的参数学习或潜在状态推断通常都涉及复杂潜在状态后验分布的计算。本文基于变分序贯蒙特卡洛方法（VSMC）展开研究，该方法通过结合粒子方法与变分推断，实现了高效且精确的模型参数估计与贝叶斯潜在状态推断。采用离线模式运行的标准VSMC需反复重新处理给定批次数据，而我们利用随机逼近技术，将VSMC代理ELBO梯度的逼近过程在时间维度上进行分解，从而能够处理数据流的在线学习场景。由此提出的在线VSMC算法可完全实时地高效执行参数估计与粒子提议分布自适应。此外，我们给出了描述该算法在数据量趋于无穷时收敛性质的严格理论证明，并通过数值实验展示了其优异的收敛特性与在批量处理场景中的实用价值。