# A unifying framework for generalised Bayesian online learning in non-stationary environments

arXiv: https://arxiv.org/abs/2411.10153 · HTML: https://mlsanity.com/paper/2411.10153/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 82 references that are in the map.
- First posted on arXiv 15 Nov 2024.

## Builds on (most cited first, 30 of 31)

- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [The Bayesian Learning Rule](https://mlsanity.com/paper/2107.04562/) (2021)
- [Online Continual Learning with Natural Distribution Shifts: An Empirical Study with Visual Data](https://mlsanity.com/paper/2108.09020/) (2021)
- [An Evaluation of Change Point Detection Algorithms](https://mlsanity.com/paper/2003.06222/) (2020)
- [Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks](https://mlsanity.com/paper/1301.3853/) (2013)
- [SLANG: Fast Structured Covariance Approximations for Bayesian Deep Learning with Natural Gradient](https://mlsanity.com/paper/1811.04504/) (2018)
- [Online Natural Gradient as a Kalman Filter](https://mlsanity.com/paper/1703.00209/) (2017)
- [Low-rank extended Kalman filtering for online learning of neural networks from streaming data](https://mlsanity.com/paper/2305.19535/) (2023)
- [Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with β-Divergences](https://mlsanity.com/paper/1806.02261/) (2018)
- [Non-Stationary Bandit Learning via Predictive Sampling](https://mlsanity.com/paper/2205.01970/) (2022)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Detecting and Adapting to Irregular Distribution Shifts in Bayesian Online Learning](https://mlsanity.com/paper/2012.08101/) (2020)
- [The Ensemble Kalman Filter: A Signal Processing Perspective](https://mlsanity.com/paper/1702.08061/) (2017)
- [Non-Stationary Learning of Neural Networks with Automatic Soft Parameter Reset](https://mlsanity.com/paper/2411.04034/) (2024)
- [Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patching](https://mlsanity.com/paper/2405.20799/) (2024)
- [Efficient Online Bayesian Inference for Neural Bandits](https://mlsanity.com/paper/2112.00195/) (2021)
- [Kalman Filter for Online Classification of Non-Stationary Data](https://mlsanity.com/paper/2306.08448/) (2023)
- [Bayesian Online Natural Gradient (BONG)](https://mlsanity.com/paper/2405.19681/) (2024)
- [Spatio-temporal Bayesian On-line Changepoint Detection with Model Selection](https://mlsanity.com/paper/1805.05383/) (2018)
- [Thompson Sampling in Switching Environments with Bayesian Online Change Point Detection](https://mlsanity.com/paper/1302.3721/) (2013)
- [Changepoint Detection in the Presence of Outliers](https://mlsanity.com/paper/1609.07363/) (2016)
- [The limited-memory recursive variational Gaussian approximation (L-RVGA)](https://mlsanity.com/paper/2303.14195/) (2023)
- [Nonstationary Portfolios: Diversification in the Spectral Domain](https://mlsanity.com/paper/2102.00477/) (2021)
- [Viking: Variational Bayesian Variance Tracking](https://mlsanity.com/paper/2104.10777/) (2021)
- [Robust Sequential Online Prediction with Dynamic Ensemble of Multiple Models: A Review](https://mlsanity.com/paper/2112.02374/) (2021)
- [BAM: Bayes with Adaptive Memory](https://mlsanity.com/paper/2202.02405/) (2022)
- [Adaptive time series forecasting with markovian variance switching](https://mlsanity.com/paper/2402.14684/) (2024)

## Built on by (most cited first, 5 of 5)

- [Martingale Posterior Neural Networks for Fast Sequential Decision Making](https://mlsanity.com/paper/2506.11898/) (2025)
- [A Predictive View on Streaming Hidden Markov Models](https://mlsanity.com/paper/2604.09208/) (2026)
- [Adversarial observations in probabilistic State-Space Models for robust Reinforcement Learning](https://mlsanity.com/paper/2606.20880/) (2026)
- [A probabilistic framework for online test-time adaptation](https://mlsanity.com/paper/2606.26457/) (2026)
- [Online Learning via Learned Latent Bayesian Tracking](https://mlsanity.com/paper/2609.31559/) (2026)

## Abstract (arXiv)

We propose a unifying framework for methods that perform probabilistic online learning in non-stationary environments. We call the framework BONE, which stands for generalised (B)ayesian (O)nline learning in (N)on-stationary (E)nvironments. BONE provides a common structure to tackle a variety of problems, including online continual learning, prequential forecasting, and contextual bandits. The framework requires specifying three modelling choices: (i) a model for measurements (e.g., a neural network), (ii) an auxiliary process to model non-stationarity (e.g., the time since the last changepoint), and (iii) a conditional prior over model parameters (e.g., a multivariate Gaussian). The framework also requires two algorithmic choices, which we use to carry out approximate inference under this framework: (i) an algorithm to estimate beliefs (posterior distribution) about the model parameters given the auxiliary variable, and (ii) an algorithm to estimate beliefs about the auxiliary variable. We show how the modularity of our framework allows for many existing methods to be reinterpreted as instances of BONE, and it allows us to propose new methods. We compare experimentally existing methods with our proposed new method on several datasets, providing insights into the situations that make each method more suitable for a specific task. We provide a Jax open source library to facilitate the adoption of this framework.