# Bayesian Learning for Dynamic Inference

arXiv: https://arxiv.org/abs/2301.00032 · HTML: https://mlsanity.com/paper/2301.00032/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 30 Dec 2022.

## Builds on (most cited first, 6 of 6)

- [Behavioral Cloning from Observation](https://mlsanity.com/paper/1805.01954/) (2018)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [The Statistical Complexity of Interactive Decision Making](https://mlsanity.com/paper/2112.13487/) (2021)
- [Model-Based Bayesian Exploration](https://mlsanity.com/paper/1301.6690/) (2013)
- [Dual Control for Approximate Bayesian Reinforcement Learning](https://mlsanity.com/paper/1510.03591/) (2015)
- [Online learning with dynamics: A minimax perspective](https://mlsanity.com/paper/2012.01705/) (2020)

## Built on by (most cited first, 1 of 1)

- [One if by Land, Two if by Sea, Three if by Four Seas, and More to Come -- Values of Perception, Prediction, Communication, and Common Sense in Decision Making](https://mlsanity.com/paper/2601.06077/) (2025)

## Abstract (arXiv)

The traditional statistical inference is static, in the sense that the estimate of the quantity of interest does not affect the future evolution of the quantity. In some sequential estimation problems however, the future values of the quantity to be estimated depend on the estimate of its current value. This type of estimation problems has been formulated as the dynamic inference problem. In this work, we formulate the Bayesian learning problem for dynamic inference, where the unknown quantity-generation model is assumed to be randomly drawn according to a random model parameter. We derive the optimal Bayesian learning rules, both offline and online, to minimize the inference loss. Moreover, learning for dynamic inference can serve as a meta problem, such that all familiar machine learning problems, including supervised learning, imitation learning and reinforcement learning, can be cast as its special cases or variants. Gaining a good understanding of this unifying meta problem thus sheds light on a broad spectrum of machine learning problems as well.