Online optimization has gained increasing interest due to its capability of tracking real-world streaming data. Although online optimization methods have been widely studied in the setting of frequentist statistics, few works have considered online optimization with the Bayesian sampling problem. In this paper, we study an Online Particle-based Variational Inference (OPVI) algorithm that uses a set of particles to represent the approximating distribution. To reduce the gradient error caused by the use of stochastic approximation, we include a sublinear increasing batch-size method to reduce the variance. To track the performance of the OPVI algorithm with respect to a sequence of dynamically changing target posterior, we provide a detailed theoretical analysis from the perspective of Wasserstein gradient flow with a dynamic regret. Synthetic and Bayesian Neural Network experiments show that the proposed algorithm achieves better results than naively applying existing Bayesian sampling methods in the online setting.

翻译：在线优化因其能够追踪真实世界流式数据的能力而日益受到关注。尽管在线优化方法在频率统计框架下已被广泛研究，但将在线优化应用于贝叶斯采样问题的研究较少。本文研究了一种基于粒子的在线变分推理（OPVI）算法，该算法使用一组粒子来表示近似分布。为降低随机近似导致的梯度误差，我们引入了一种次线性递增批次大小的方法来减小方差。为追踪OPVI算法在一系列动态变化的目标后验上的性能，我们基于带有动态遗憾的Wasserstein梯度流提供了详细的理论分析。合成实验与贝叶斯神经网络实验表明，与在线场景下直接应用现有贝叶斯采样方法相比，所提算法取得了更优的结果。