# On efficient computation in active inference

arXiv: https://arxiv.org/abs/2307.00504 · HTML: https://mlsanity.com/paper/2307.00504/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 70 references that are in the map.
- First posted on arXiv 2 Jul 2023.

## Builds on (most cited first, 24 of 24)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Active inference on discrete state-spaces: a synthesis](https://mlsanity.com/paper/2001.07203/) (2020)
- [Deep active inference agents using Monte-Carlo methods](https://mlsanity.com/paper/2006.04176/) (2020)
- [Sophisticated Inference](https://mlsanity.com/paper/2006.04120/) (2020)
- [On the Relationship Between Active Inference and Control as Inference](https://mlsanity.com/paper/2006.12964/) (2020)
- [A free energy principle for a particular physics](https://mlsanity.com/paper/1906.10184/) (2019)
- [The free energy principle made simpler but not too simple](https://mlsanity.com/paper/2201.06387/) (2022)
- [The Free Energy Principle for Perception and Action: A Deep Learning Perspective](https://mlsanity.com/paper/2207.06415/) (2022)
- [Active Inference and Behavior Trees for Reactive Action Planning and Execution in Robotics](https://mlsanity.com/paper/2011.09756/) (2020)
- [Learning Perception and Planning with Deep Active Inference](https://mlsanity.com/paper/2001.11841/) (2020)
- [Branching Time Active Inference: the theory and its generality](https://mlsanity.com/paper/2111.11107/) (2021)
- [An empirical evaluation of active inference in multi-armed bandits](https://mlsanity.com/paper/2101.08699/) (2021)
- [Exploration and preference satisfaction trade-off in reward-free learning](https://mlsanity.com/paper/2106.04316/) (2021)
- [Information is Power: Intrinsic Control via Information Capture](https://mlsanity.com/paper/2112.03899/) (2021)
- [SMiRL: Surprise Minimizing Reinforcement Learning in Unstable Environments](https://mlsanity.com/paper/1912.05510/) (2019)
- [Branching Time Active Inference: empirical study and complexity class analysis](https://mlsanity.com/paper/2111.11276/) (2021)
- [Bayesian brains and the R'enyi divergence](https://mlsanity.com/paper/2107.05438/) (2021)
- [Active Inference for Stochastic Control](https://mlsanity.com/paper/2108.12245/) (2021)
- [Active inference, Bayesian optimal design, and expected utility](https://mlsanity.com/paper/2110.04074/) (2021)
- [Designing explainable artificial intelligence with active inference: A framework for transparent introspection and decision-making](https://mlsanity.com/paper/2306.04025/) (2023)
- [Neural dynamics under active inference: plausibility and efficiency of information processing](https://mlsanity.com/paper/2001.08028/) (2020)
- [Online distributed algorithms for seeking generalized Nash equilibria in dynamic environments](https://mlsanity.com/paper/2004.00525/) (2020)
- [Goal-directed Planning and Goal Understanding by Active Inference: Evaluation Through Simulated and Physical Robot Experiments](https://mlsanity.com/paper/2202.09976/) (2022)
- [Modelling non-reinforced preferences using selective attention](https://mlsanity.com/paper/2207.13699/) (2022)

## Built on by (most cited first, 15 of 15)

- [R-AIF: Solving Sparse-Reward Robotic Tasks from Pixels with Active Inference and World Models](https://mlsanity.com/paper/2409.14216/) (2024)
- [Expected Free Energy-based Planning as Variational Inference](https://mlsanity.com/paper/2504.14898/) (2025)
- [A Message Passing Realization of Expected Free Energy Minimization](https://mlsanity.com/paper/2508.02197/) (2025)
- [Active Inference and Intentional Behaviour](https://mlsanity.com/paper/2312.07547/) (2023)
- [On Predictive planning and counterfactual learning in active inference](https://mlsanity.com/paper/2403.12417/) (2024)
- [Active Inference and Human--Computer Interaction](https://mlsanity.com/paper/2412.14741/) (2024)
- [Deep Active Inference Agents for Delayed and Long-Horizon Environments](https://mlsanity.com/paper/2505.19867/) (2025)
- [Free Energy Projective Simulation (FEPS): Active inference with interpretability](https://mlsanity.com/paper/2411.14991/) (2024)
- [What Type of Inference is Active Inference?](https://mlsanity.com/paper/2606.04935/) (2026)
- [Active Inference Meeting Energy-Efficient Control of Parallel and Identical Machines](https://mlsanity.com/paper/2406.09322/) (2024)
- [Contemplative Artificial Intelligence](https://mlsanity.com/paper/2504.15125/) (2025)
- [Dynamic planning in hierarchical active inference](https://mlsanity.com/paper/2402.11658/) (2024)
- [A memory-based active inference model of DishBrain-like adaptive behaviour](https://mlsanity.com/paper/2508.06980/) (2025)
- [Expected Free Energy-based Planning as Variational Inference](https://mlsanity.com/paper/2606.20658/) (2026)
- [Sophisticated Policies from Epistemic Priors](https://mlsanity.com/paper/2607.19518/) (2026)

## Abstract (arXiv)

Despite being recognized as neurobiologically plausible, active inference faces difficulties when employed to simulate intelligent behaviour in complex environments due to its computational cost and the difficulty of specifying an appropriate target distribution for the agent. This paper introduces two solutions that work in concert to address these limitations. First, we present a novel planning algorithm for finite temporal horizons with drastically lower computational complexity. Second, inspired by Z-learning from control theory literature, we simplify the process of setting an appropriate target distribution for new and existing active inference planning schemes. Our first approach leverages the dynamic programming algorithm, known for its computational efficiency, to minimize the cost function used in planning through the Bellman-optimality principle. Accordingly, our algorithm recursively assesses the expected free energy of actions in the reverse temporal order. This improves computational efficiency by orders of magnitude and allows precise model learning and planning, even under uncertain conditions. Our method simplifies the planning process and shows meaningful behaviour even when specifying only the agent's final goal state. The proposed solutions make defining a target distribution from a goal state straightforward compared to the more complicated task of defining a temporally informed target distribution. The effectiveness of these methods is tested and demonstrated through simulations in standard grid-world tasks. These advances create new opportunities for various applications.