# Expected Free Energy-based Planning as Variational Inference

arXiv: https://arxiv.org/abs/2606.20658 · HTML: https://mlsanity.com/paper/2606.20658/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 50 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [Minigrid & Miniworld: Modular & Customizable Reinforcement Learning Environments for Goal-Oriented Tasks](https://mlsanity.com/paper/2306.13831/) (2023)
- [Active inference on discrete state-spaces: a synthesis](https://mlsanity.com/paper/2001.07203/) (2020)
- [Sophisticated Inference](https://mlsanity.com/paper/2006.04120/) (2020)
- [A free energy principle for a particular physics](https://mlsanity.com/paper/1906.10184/) (2019)
- [pymdp: A Python library for active inference in discrete state spaces](https://mlsanity.com/paper/2201.03904/) (2022)
- [Path integrals, particular kinds, and strange things](https://mlsanity.com/paper/2210.12761/) (2022)
- [Reactive Message Passing for Scalable Bayesian Inference](https://mlsanity.com/paper/2112.13251/) (2021)
- [Branching Time Active Inference: the theory and its generality](https://mlsanity.com/paper/2111.11107/) (2021)
- [On efficient computation in active inference](https://mlsanity.com/paper/2307.00504/) (2023)
- [Model-free, Model-based, and General Intelligence](https://mlsanity.com/paper/1806.02308/) (2018)
- [Active Inference as a Model of Agency](https://mlsanity.com/paper/2401.12917/) (2024)
- [What type of inference is planning?](https://mlsanity.com/paper/2406.17863/) (2024)
- [Realising Synthetic Active Inference Agents, Part II: Variational Message Updates](https://mlsanity.com/paper/2306.02733/) (2023)
- [Kullback-Leibler control for discrete-time nonlinear systems on continuous spaces](https://mlsanity.com/paper/2203.12864/) (2022)
- [Realising Synthetic Active Inference Agents, Part I: Epistemic Objectives and Graphical Specification Language](https://mlsanity.com/paper/2306.08014/) (2023)
- [On Predictive planning and counterfactual learning in active inference](https://mlsanity.com/paper/2403.12417/) (2024)
- [Toward Design of Synthetic Active Inference Agents by Mere Mortals](https://mlsanity.com/paper/2307.14145/) (2023)

## Abstract (arXiv)

Planning under uncertainty requires agents to balance goal achievement with information gathering. Active inference addresses this through the Expected Free Energy (EFE), a cost function that unifies instrumental and epistemic objectives. However, existing EFE-based methods typically employ specialized optimization procedures that are difficult to extend or analyze. In this paper, we show that EFE-based planning can be formulated as Variational Free Energy minimization on a generative model augmented with epistemic priors. Our main result demonstrates that minimizing a Variational Free Energy functional with appropriately chosen priors yields a decomposition into expected plan costs (the EFE) plus a complexity term. This formulation reinforces theoretical consistency with the Free Energy Principle by casting planning as the same inferential process that governs perception and learning. We validate our approach on three environments of increasing complexity: a deterministic T-maze, a stochastic Reactivity Maze, and a partially observable MiniGrid DoorKey-8x8 environment. The experiments demonstrate that the epistemic priors induce information-seeking behavior, that the variational formulation yields policy-based inference outperforming plan-based methods under stochastic transitions, and that temporal factorization enables scalability to environments where existing tabular active inference methods cannot operate.