# Chance-Constrained Active Inference

arXiv: https://arxiv.org/abs/2102.08792 · HTML: https://mlsanity.com/paper/2102.08792/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 17 Feb 2021.

## Builds on (most cited first, 11 of 11)

- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [A Tour of Reinforcement Learning: The View from Continuous Control](https://mlsanity.com/paper/1806.09460/) (2018)
- [Deep active inference agents using Monte-Carlo methods](https://mlsanity.com/paper/2006.04176/) (2020)
- [Reinforcement Learning through Active Inference](https://mlsanity.com/paper/2002.12636/) (2020)
- [Deep Active Inference](https://mlsanity.com/paper/1709.02341/) (2017)
- [On the Relationship Between Active Inference and Control as Inference](https://mlsanity.com/paper/2006.12964/) (2020)
- [An empirical evaluation of active inference in multi-armed bandits](https://mlsanity.com/paper/2101.08699/) (2021)
- [A Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms](https://mlsanity.com/paper/1811.03407/) (2018)
- [Active Inference or Control as Inference? A Unifying View](https://mlsanity.com/paper/2010.00262/) (2020)
- [Application of the Free Energy Principle to Estimation and Control](https://mlsanity.com/paper/1910.09823/) (2019)
- [The modularity of action and perception revisited using control theory and active inference](https://mlsanity.com/paper/1806.02649/) (2018)

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

- [pymdp: A Python library for active inference in discrete state spaces](https://mlsanity.com/paper/2201.03904/) (2022)
- [Realising Synthetic Active Inference Agents, Part II: Variational Message Updates](https://mlsanity.com/paper/2306.02733/) (2023)
- [Bayesian brains and the R'enyi divergence](https://mlsanity.com/paper/2107.05438/) (2021)
- [Active Inference and Epistemic Value in Graphical Models](https://mlsanity.com/paper/2109.00541/) (2021)
- [Expected free energy as an information constraint on the Bethe Lagrangian](https://mlsanity.com/paper/2608.17167/) (2026)

## Abstract (arXiv)

Active Inference (ActInf) is an emerging theory that explains perception and action in biological agents, in terms of minimizing a free energy bound on Bayesian surprise. Goal-directed behavior is elicited by introducing prior beliefs on the underlying generative model. In contrast to prior beliefs, which constrain all realizations of a random variable, we propose an alternative approach through chance constraints, which allow for a (typically small) probability of constraint violation, and demonstrate how such constraints can be used as intrinsic drivers for goal-directed behavior in ActInf. We illustrate how chance-constrained ActInf weights all imposed (prior) constraints on the generative model, allowing e.g., for a trade-off between robust control and empirical chance constraint violation. Secondly, we interpret the proposed solution within a message passing framework. Interestingly, the message passing interpretation is not only relevant to the context of ActInf, but also provides a general purpose approach that can account for chance constraints on graphical models. The chance constraint message updates can then be readily combined with other pre-derived message update rules, without the need for custom derivations. The proposed chance-constrained message passing framework thus accelerates the search for workable models in general, and can be used to complement message-passing formulations on generative neural models.