Active Inference for Physical AI Agents -- An Engineering Perspective

Bert de Vries

stat.MLMar 21, 2026

Active Inference for Physical AI Agents -- An Engineering Perspective

Authors: Bert de Vries

Organizations: Department of Electrical Engineering, Eindhoven University of Technology, the Netherlands

Abstract

Physical AI agents, such as robots and other embodied systems operating under tight and fluctuating resource constraints, remain far less capable than biological agents in open-ended real-world environments. This paper argues that Active Inference (AIF), grounded in the Free Energy Principle, offers a principled foundation for closing that gap. We develop this argument from first principles, following a chain from probability theory through Bayesian machine learning and variational inference to active inference and reactive message passing. From the FEP perspective, systems that maintain their structural and functional integrity over time can, under suitable assumptions, be described as minimizing variational free energy (VFE), and AIF operationalizes this by unifying perception, learning, planning, and control within a single computational objective. We show that VFE minimization is naturally realized by reactive message passing on factor graphs, where inference emerges from local, parallel computations. This realization is well matched to the constraints of physical operation, including hard deadlines, asynchronous data, fluctuating power budgets, and changing environments. Because reactive message passing is event-driven, interruptible, and locally adaptable, performance degrades gracefully under reduced resources while model structure can adjust online. We further show that, under suitable coupling and coarse-graining conditions, coupled AIF agents can be described as higher-level AIF agents, yielding a homogeneous architecture based on the same message-passing primitive across scales. Our contribution is not empirical benchmarking, but a clear theoretical and architectural case for the engineering community.

Figures & tables

Figure 1: Screenshot from the RoboCup 2025 Finals in Brazil (“Humanoid Robot Play Football” category), in which China’s Booster Robotics team won the tournament. The robots played fully autonomously. Video: “Humanoid Robot Play Football at RoboCup 2025 Finals in Brazil,” uploaded by Chris Wabs on 20 July 2025. Available at https://youtu.be/3Gyx-zT4gog?si=1kwZT1ikCm5pl2Lq .

Panel of Figure 2 — Figure 2: Conceptual pathway developed in this paper. Each stage builds on the previous one, culminating in a distributed, resource-adaptive architecture for physical AI agents. The annotations below each stage summarize the key property contributed at that level.

Panel of Figure 3 — Figure 3: Agent–environment interaction under the Free Energy Principle. States are partitioned into external $x$ (environment), sensory $y$ , control $u$ , and internal $s$ (agent). Sensory and control states jointly form the Markov blanket , satisfying $x\perp s\mid(y,u)$ . The perception–action loop runs clockwise: external states generate sensory inputs; the agent infers a posterior $q(x|s)\approx p(x|y,u)$ over external states (perception); internal states plan by forming a posterior $q(u)\propto e^{-G(u)}$ over control states, where $G(u)$ is the Expected Free Energy ( 33 ); and the sampled action modifies the environment.

Panel of Figure 4 — Figure 4: Nested active inference: coarse-graining two coupled AIF agents into a collective AIF agent. Left: Two agents $A_{1}$ and $A_{2}$ , each with partition $(y_{i},x_{i},u_{i},s_{i})$ . External states are split into outward-facing $x_{i}^{\mathrm{out}}$ (red), which interface with the environment beyond the ensemble, and inward-facing $x_{i}^{\mathrm{in}}$ (orange), which mediate inter-agent coupling. Similarly, blanket states are split into outward-facing $(y_{i}^{\mathrm{out}},u_{i}^{\mathrm{out}})$ (gray) and inward-facing $(y_{i}^{\mathrm{in}},u_{i}^{\mathrm{in}})$ (blue). Inter-agent influence follows the chain $s_{i}\to u_{i}^{\mathrm{in}}\to x_{i}^{\mathrm{in}}\leftrightarrow x_{j}^{\mathrm{in}}\to y_{j}^{\mathrm{in}}\to s_{j}$ . Right: Under conditions E1–E3, the ensemble admits a collective Markov-blanketed partition ( 35 ). Outward-facing blanket states form the collective blanket $(y_{\mathrm{col}},u_{\mathrm{col}})$ , outward-facing external states form $x_{\mathrm{col}}$ , and all inward-facing states together with the individual internal states are absorbed into $s_{\mathrm{col}}$ .

Panel of Figure 5 — Figure 5: A Forney-style factor graph with messages $\mu_{ai}(x_{i})$ , denoting the message from node $f_{a}$ to edge $x_{i}$ , and the resulting marginal $\bar{f}(x_{3})$ as defined in ( 41 ).

Panel of Figure 6 — Figure 6: A robot football team as coupled AIF agents. Three players $P_{1}$ , $P_{2}$ , $P_{3}$ , each an AIF agent with sensory states $y_{i}$ , internal states $s_{i}$ , and control states $u_{i}$ . Each player connects to the external environment (pitch, ball, opponents) through outward-facing states $x_{i}^{\mathrm{out}}$ (red arrows). Adjacent players are coupled through shared inter-agent spaces $x_{12}^{\mathrm{in}}$ and $x_{23}^{\mathrm{in}}$ (orange). The orange arrows represent the inward-facing components of $y_{i}$ and $u_{i}$ : each player’s inward actions $u_{i}^{\mathrm{in}}$ (e.g., broadcast signals) enter the shared space, while inward observations $y_{i}^{\mathrm{in}}$ (e.g., received messages) flow back from it. Players $P_{1}$ and $P_{3}$ interact only indirectly, through $P_{2}$ .

Aspect	Classical approach	AIF approach	Why it matters
Objective	Separate objectives for perception, control, and learning	Single variational free energy objective spanning perception, control, and learning	Reduces fragmentation and ad hoc interfaces
Architecture	Specialized modules with hand-designed couplings	One generative model with local message passing updates	Supports end-to-end coherence under uncertainty
Uncertainty	Often split across estimator, planner, and controller	Handled directly through probabilistic inference and (expected) free energy	Keeps epistemic and goal-directed behavior in one formalism
Learning	Commonly added as a separate subsystem or offline stage	Can be formulated as active learning of parameters and, in principle, structure	Aligns adaptation with goals and uncertainty
Exploration	Typically heuristic or bonus-based	Driven by risk, ambiguity, and novelty in expected free energy	Avoids bolting exploration onto a separate control stack
Reward / preferences	Externally specified reward function $R(x,u)$	Preference model $\hat{p}(x)$ within the generative model	Avoids a separate reward-design layer

Table 1: Conceptual comparison between classical modular architectures for physical AI and the active-inference-based architecture argued for in this paper. Classical methods work well in stable, narrowly defined settings; the claim here is that active inference is a better architectural fit for embodied agents operating under fluctuating real-world constraints.

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