# Expected Free Energy-based Planning as Variational Inference

arXiv: https://arxiv.org/abs/2504.14898 · HTML: https://mlsanity.com/paper/2504.14898/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 50 references that are in the map.
- First posted on arXiv 21 Apr 2025.

## 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)

## Built on by (most cited first, 10 of 10)

- [A Message Passing Realization of Expected Free Energy Minimization](https://mlsanity.com/paper/2508.02197/) (2025)
- [Active Inference for Physical AI Agents -- An Engineering Perspective](https://mlsanity.com/paper/2603.20927/) (2026)
- [What Type of Inference is Active Inference?](https://mlsanity.com/paper/2606.04935/) (2026)
- [Message passing-based inference in an autoregressive active inference agent](https://mlsanity.com/paper/2509.25482/) (2025)
- [Active Inference as a Convex Markov Decision Process](https://mlsanity.com/paper/2607.20152/) (2026)
- [Active Inference is a Subtype of Variational Inference](https://mlsanity.com/paper/2511.18955/) (2025)
- [Expected Free Energy as Belief-Dependent Utility for rho-POMDPs](https://mlsanity.com/paper/2607.16981/) (2026)
- [Sophisticated Policies from Epistemic Priors](https://mlsanity.com/paper/2607.19518/) (2026)
- [Information Geometry of Message Passing](https://mlsanity.com/paper/2608.15922/) (2026)
- [Expected free energy as an information constraint on the Bethe Lagrangian](https://mlsanity.com/paper/2608.17167/) (2026)

## Abstract (arXiv)

We address the problem of planning under uncertainty, where an agent must choose actions that not only achieve desired outcomes but also reduce uncertainty. Traditional methods often treat exploration and exploitation as separate objectives, lacking a unified inferential foundation. Active inference, grounded in the Free Energy Principle, provides such a foundation by minimizing Expected Free Energy (EFE), a cost function that combines utility with epistemic drives, such as ambiguity resolution and novelty seeking. However, the computational burden of EFE minimization had remained a significant obstacle to its scalability. In this paper, we show that EFE-based planning arises naturally from minimizing a variational free energy functional on a generative model augmented with preference and epistemic priors. This result reinforces theoretical consistency with the Free Energy Principle by casting planning under uncertainty itself as a form of variational inference. Our formulation yields policies that jointly support goal achievement and information gain, while incorporating a complexity term that accounts for bounded computational resources. This unifying framework connects and extends existing methods, enabling scalable, resource-aware implementations of active inference agents.