Deep active inference agents using Monte-Carlo methods
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Abstract (arXiv)
Active inference is a Bayesian framework for understanding biological intelligence. The underlying theory brings together perception and action under one single imperative: minimizing free energy. However, despite its theoretical utility in explaining intelligence, computational implementations have been restricted to low-dimensional and idealized situations. In this paper, we present a neural architecture for building deep active inference agents operating in complex, continuous state-spaces using multiple forms of Monte-Carlo (MC) sampling. For this, we introduce a number of techniques, novel to active inference. These include: i) selecting free-energy-optimal policies via MC tree search, ii) approximating this optimal policy distribution via a feed-forward `habitual' network, iii) predicting future parameter belief updates using MC dropouts and, finally, iv) optimizing state transition precision (a high-end form of attention). Our approach enables agents to learn environmental dynamics efficiently, while maintaining task performance, in relation to reward-based counterparts. We illustrate this in a new toy environment, based on the dSprites data-set, and demonstrate that active inference agents automatically create disentangled representations that are apt for modeling state transitions. In a more complex Animal-AI environment, our agents (using the same neural architecture) are able to simulate future state transitions and actions (i.e., plan), to evince reward-directed navigation - despite temporary suspension of visual input. These results show that deep active inference - equipped with MC methods - provides a flexible framework to develop biologically-inspired intelligent agents, with applications in both machine learning and cognitive science.
Key facts. Cited by 72 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Jun 2020.
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Citing papers per year: 2021: 20; 2022: 11; 2023: 12; 2024: 14; 2025: 8; 2026: 7.
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- 2021Active Inference in Robotics and Artificial Agents: Survey and Challengescited by 52
- 2022pymdp: A Python library for active inference in discrete state spacescited by 39
- 2023World Models and Predictive Coding for Cognitive and Developmental Robotics: Frontiers and Challengescited by 35
- 2022The Free Energy Principle for Perception and Action: A Deep Learning Perspectivecited by 24
- 2021Contrastive Active Inferencecited by 21
- 2021Branching Time Active Inference: the theory and its generalitycited by 15
- 2023On efficient computation in active inferencecited by 15
- 2021An empirical evaluation of active inference in multi-armed banditscited by 12
- 2021Exploration and preference satisfaction trade-off in reward-free learningcited by 12
- 2024Active Inference as a Model of Agencycited by 12
- 2021Information is Power: Intrinsic Control via Information Capturecited by 11
- 2021Understanding the Origin of Information-Seeking Exploration in Probabilistic Objectives for Controlcited by 10
38 more
- 2024R-AIF: Solving Sparse-Reward Robotic Tasks from Pixels with Active Inference and World Modelscited by 10
- 2021Applications of the Free Energy Principle to Machine Learning and Neurosciencecited by 9
- 2021Branching Time Active Inference: empirical study and complexity class analysiscited by 9
- 2023A Unified View on Solving Objective Mismatch in Model-Based Reinforcement Learningcited by 9
- 2023Supervised structure learningcited by 9
- 2021Prior Preference Learning from Experts:Designing a Reward with Active Inferencecited by 8
- 2022Complex behavior from intrinsic motivation to occupy action-state path spacecited by 7
- 2021Bayesian brains and the R'enyi divergencecited by 6
- 2021Active Inference for Stochastic Controlcited by 6
- 2021Active inference, Bayesian optimal design, and expected utilitycited by 6
- 2022Disentangling Shape and Pose for Object-Centric Deep Active Inference Modelscited by 6
- 2023Resolving uncertainty on the fly: Modeling adaptive driving behavior as active inferencecited by 6
- 2021Chance-Constrained Active Inferencecited by 5
- 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
- 2023Deconstructing deep active inferencecited by 5
- 2022Goal-directed Planning and Goal Understanding by Active Inference: Evaluation Through Simulated and Physical Robot Experimentscited by 4
- 2023Integrating cognitive map learning and active inference for planning in ambiguous environmentscited by 4
- 2024SPO: Sequential Monte Carlo Policy Optimisationcited by 4
- 2024On Predictive planning and counterfactual learning in active inferencecited by 4
- 2026ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inferencecited by 4
- 2022Successor Representation Active Inferencecited by 3
- 2023Habits and goals in synergy: a variational Bayesian framework for behaviorcited by 3
- 2025Deep Active Inference Agents for Delayed and Long-Horizon Environmentscited by 3
- 2021Active Inference Tree Search in Large POMDPscited by 2
- 2021Goal-Directed Planning by Reinforcement Learning and Active Inferencecited by 2
- 2021Deep Active Inference for Pixel-Based Discrete Control: Evaluation on the Car Racing Problemcited by 2
- 2021Branching Time Active Inference with Bayesian Filteringcited by 2
- 2022Recursive Neural Programs: Variational Learning of Image Grammars and Part-Whole Hierarchiescited by 2
- 2022Multi-Modal and Multi-Factor Branching Time Active Inferencecited by 2
- 2023Sophisticated Learning: A novel algorithm for active learning during model-based planningcited by 2
- 2024Object-centric proto-symbolic behavioural reasoning from pixelscited by 2
- 2026The SIGReg Objective as Variational Free Energy: A Theoretical Active-Inference Account of JEPA World Modelscited by 2
- 2021Realising Active Inference in Variational Message Passing: the Outcome-blind Certainty Seekercited by 1
- 2022Modelling non-reinforced preferences using selective attentioncited by 1
- 2023A general Markov decision process formalism for action-state entropy-regularized reward maximizationcited by 1
- 2023Learning Successor Features with Distributed Hebbian Temporal Memorycited by 1
- 2024Active Inference Meeting Energy-Efficient Control of Parallel and Identical Machinescited by 1
- 2024Free Energy Projective Simulation (FEPS): Active inference with interpretabilitycited by 1
50 most cited of 72 All 72 (JSON)
- 2026Expected Free Energy-based Informative Path Planning for Robotic Mars Exploration14 Aug 2026
- 2026Active Inference as a Convex Markov Decision Process22 Jul 2026
- 2026Expected Free Energy as Belief-Dependent Utility for rho-POMDPs18 Jul 2026
- 2026The SIGReg Objective as Variational Free Energy: A Theoretical Active-Inference Account of JEPA World Models15 Jul 2026
- 2026Affinity Is Not Enough: Recovering the Free Energy Principle in Mixture-of-Experts1 May 2026
- 2026ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inference27 Feb 2026
- 2026Distributional Active Inference28 Jan 2026
- 2025Prior preferences in active inference agents: soft, hard, and goal shaping2 Dec 2025
- 2025Real-World Robot Control by Deep Active Inference With a Temporally Hierarchical World Model1 Dec 2025
- 2025Curiosity-Driven Development of Action and Language in Robots Through Self-Exploration6 Oct 2025
- 2025A memory-based active inference model of DishBrain-like adaptive behaviour9 Aug 2025
- 2025Multi-dimensional Autoscaling of Processing Services: A Comparison of Agent-based Methods12 Jun 2025
38 more
- 2025Deep Active Inference Agents for Delayed and Long-Horizon Environments26 May 2025
- 2025An Active Inference perspective on Neurofeedback Training6 May 2025
- 2025Boosting MCTS with Free Energy Minimization22 Jan 2025
- 2024Object-centric proto-symbolic behavioural reasoning from pixels26 Nov 2024
- 2024Free Energy Projective Simulation (FEPS): Active inference with interpretability22 Nov 2024
- 2024R-AIF: Solving Sparse-Reward Robotic Tasks from Pixels with Active Inference and World Models21 Sep 2024
- 2024Environment-Centric Active Inference23 Aug 2024
- 2024CogNarr Ecosystem: Facilitating Group Cognition at Scale11 Jul 2024
- 2024Online Pareto-Optimal Decision-Making for Complex Tasks using Active Inference17 Jun 2024
- 2024Active Inference Meeting Energy-Efficient Control of Parallel and Identical Machines13 Jun 2024
- 2024On Predictive planning and counterfactual learning in active inference19 Mar 2024
- 2024Seeing Through Uncertainty: Free-Energy-Inspired Real-Time Adaptation for Robust Visual Navigation4 Mar 2024
- 2024When in Doubt, Think Slow: Iterative Reasoning with Latent Imagination23 Feb 2024
- 2024Dynamic planning in hierarchical active inference18 Feb 2024
- 2024SPO: Sequential Monte Carlo Policy Optimisation12 Feb 2024
- 2024Deep hybrid models: infer and plan in a dynamic world1 Feb 2024
- 2024Active Inference as a Model of Agency23 Jan 2024
- 2023Supervised structure learning17 Nov 2023
- 2023Resolving uncertainty on the fly: Modeling adaptive driving behavior as active inference10 Nov 2023
- 2023Learning Successor Features with Distributed Hebbian Temporal Memory20 Oct 2023
- 2023A Unified View on Solving Objective Mismatch in Model-Based Reinforcement Learning10 Oct 2023
- 2023Integrating cognitive map learning and active inference for planning in ambiguous environments16 Aug 2023
- 2023Sophisticated Learning: A novel algorithm for active learning during model-based planning15 Aug 2023
- 2023On efficient computation in active inference2 Jul 2023
- 2023Active Inference in Hebbian Learning Networks8 Jun 2023
- 2023Habits and goals in synergy: a variational Bayesian framework for behavior11 Apr 2023
- 2023Deconstructing deep active inference2 Mar 2023
- 2023A general Markov decision process formalism for action-state entropy-regularized reward maximization2 Feb 2023
- 2023World Models and Predictive Coding for Cognitive and Developmental Robotics: Frontiers and Challenges14 Jan 2023
- 2022Disentangling Shape and Pose for Object-Centric Deep Active Inference Models16 Sep 2022
- 2022Efficient search of active inference policy spaces using k-means6 Sep 2022
- 2022Modelling non-reinforced preferences using selective attention25 Jul 2022
- 2022Successor Representation Active Inference20 Jul 2022
- 2022The Free Energy Principle for Perception and Action: A Deep Learning Perspective13 Jul 2022
- 2022Multi-Modal and Multi-Factor Branching Time Active Inference24 Jun 2022
- 2022Recursive Neural Programs: Variational Learning of Image Grammars and Part-Whole Hierarchies16 Jun 2022
- 2022Complex behavior from intrinsic motivation to occupy action-state path space20 May 2022
- 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents20 Mar 2022
50 newest of 72 All 72 (JSON)
- 2023World Models and Predictive Coding for Cognitive and Developmental Robotics: Frontiers and Challengescited by 35
- 2024Active Inference as a Model of Agencycited by 12
- 2024R-AIF: Solving Sparse-Reward Robotic Tasks from Pixels with Active Inference and World Modelscited by 10
- 2025Deep Active Inference Agents for Delayed and Long-Horizon Environmentscited by 3
- 2026The SIGReg Objective as Variational Free Energy: A Theoretical Active-Inference Account of JEPA World Modelscited by 2
- 2024When in Doubt, Think Slow: Iterative Reasoning with Latent Imaginationcited by 0
- 2025Real-World Robot Control by Deep Active Inference With a Temporally Hierarchical World Modelcited by 0
- 2026The SIGReg Objective as Variational Free Energy: A Theoretical Active-Inference Account of JEPA World Models15 Jul 2026
- 2025Real-World Robot Control by Deep Active Inference With a Temporally Hierarchical World Model1 Dec 2025
- 2025Deep Active Inference Agents for Delayed and Long-Horizon Environments26 May 2025
- 2024R-AIF: Solving Sparse-Reward Robotic Tasks from Pixels with Active Inference and World Models21 Sep 2024
- 2024When in Doubt, Think Slow: Iterative Reasoning with Latent Imagination23 Feb 2024
- 2024Active Inference as a Model of Agency23 Jan 2024
- 2023World Models and Predictive Coding for Cognitive and Developmental Robotics: Frontiers and Challenges14 Jan 2023
- 2021Active Inference in Robotics and Artificial Agents: Survey and Challengescited by 52
- 2022pymdp: A Python library for active inference in discrete state spacescited by 39
- 2022The Free Energy Principle for Perception and Action: A Deep Learning Perspectivecited by 24
- 2021Contrastive Active Inferencecited by 21
- 2021Branching Time Active Inference: the theory and its generalitycited by 15
- 2023On efficient computation in active inferencecited by 15
- 2021An empirical evaluation of active inference in multi-armed banditscited by 12
- 2021Information is Power: Intrinsic Control via Information Capturecited by 11
- 2021Understanding the Origin of Information-Seeking Exploration in Probabilistic Objectives for Controlcited by 10
- 2021Applications of the Free Energy Principle to Machine Learning and Neurosciencecited by 9
- 2021Branching Time Active Inference: empirical study and complexity class analysiscited by 9
- 2023A Unified View on Solving Objective Mismatch in Model-Based Reinforcement Learningcited by 9
12 most cited of 61 All 61 (JSON)
- 2026Expected Free Energy-based Informative Path Planning for Robotic Mars Exploration14 Aug 2026
- 2026Active Inference as a Convex Markov Decision Process22 Jul 2026
- 2026Expected Free Energy as Belief-Dependent Utility for rho-POMDPs18 Jul 2026
- 2026Distributional Active Inference28 Jan 2026
- 2025Prior preferences in active inference agents: soft, hard, and goal shaping2 Dec 2025
- 2025Curiosity-Driven Development of Action and Language in Robots Through Self-Exploration6 Oct 2025
- 2025A memory-based active inference model of DishBrain-like adaptive behaviour9 Aug 2025
- 2025Multi-dimensional Autoscaling of Processing Services: A Comparison of Agent-based Methods12 Jun 2025
- 2025An Active Inference perspective on Neurofeedback Training6 May 2025
- 2025Boosting MCTS with Free Energy Minimization22 Jan 2025
- 2024Object-centric proto-symbolic behavioural reasoning from pixels26 Nov 2024
- 2024Free Energy Projective Simulation (FEPS): Active inference with interpretability22 Nov 2024
12 newest of 61 All 61 (JSON)