Bayesian online learning provides a coherent framework for sequential inference. However, its theoretical understanding remains limited, particularly in the one-pass setting. Existing theoretical guarantees typically require the mini-batch sample size to diverge, a condition that fails in the one-pass regime. In this paper, we propose a new Bayesian online learning algorithm tailored to the one-pass setting, which incorporates a warm-start phase to ensure stable sequential updates. For this algorithm, we show that the sequentially updated posterior attains the optimal convergence rate. Building on this, we establish an online analogue of the Bernstein-von Mises theorem, which guarantees valid uncertainty quantification without diverging mini-batch sample sizes. Our analysis is based on a novel theoretical framework that differs fundamentally from existing approaches in the online learning literature. Numerical experiments on generalized linear models show that the proposed method matches the performance of the batch estimator while outperforming existing online procedures.

The proliferation of capable and efficient machine learning (ML) models marks one of the strongest methodological shifts in signal processing (SP) in its nearly 100-year history. ML models support the development of SP systems that represent complex, nonlinear relationships with high predictive accuracy. Adapting these models often requires sequential inference, which differs both theoretically and methodologically from the usual paradigm of ML, where data are often assumed independent and identically distributed. Gaussian processes (GPs) are a flexible yet principled framework for modeling random functions, and they have become increasingly relevant to SP as statistical and ML methods assume a more prominent role. We provide a self-contained, tutorial-style overview of GPs, with a particular focus on recent methodological advances in sequential, incremental, or streaming inference. We introduce these techniques from a signal-processing perspective while bridging them to recent advances in ML. Many of the developments we survey have direct applications to state-space modeling, sequential regression and forecasting, anomaly detection in time series, sequential Bayesian optimization, adaptive and active sensing, and sequential detection and decision-making. By organizing these advances from a signal-processing perspective, we intend to equip practitioners with practical tools and a coherent roadmap for deploying sequential GP models in real-world systems.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Learning from human feedback has been shown to improve text-to-image models. These techniques first learn a reward function that captures what humans care about in the task and then improve the models based on the learned reward function. Even though relatively simple approaches (e.g., rejection sampling based on reward scores) have been investigated, fine-tuning text-to-image models with the reward function remains challenging. In this work, we propose using online reinforcement learning (RL) to fine-tune text-to-image models. We focus on diffusion models, defining the fine-tuning task as an RL problem, and updating the pre-trained text-to-image diffusion models using policy gradient to maximize the feedbacktrained reward. Our approach, coined DPOK, integrates policy optimization with KL regularization. We conduct an analysis of KL regularization for both RL fine-tuning and supervised fine-tuning. In our experiments, we show that DPOK is generally superior to supervised fine-tuning with respect to both image-text alignment and image quality.