Proactive Active Inference: A Bayesian Decision Framework

Updated 4 February 2026

Proactive active inference is a normative Bayesian framework that minimizes expected free energy to seamlessly integrate exploration and goal-directed control.
It decomposes decision-making into epistemic value for uncertainty reduction and pragmatic value for risk-sensitive reward optimization.
The approach is applied in robotics, industrial automation, and neuroscience to enhance adaptive behavior and continual learning.

Proactive Active Inference is a normative Bayesian framework for decision-making, control, and learning under uncertainty. Distinct from purely reactive free-energy minimization, proactive active inference extends the scope of inference and action selection across future time horizons by minimizing the expected free energy (EFE) of candidate policies. This extension unifies epistemic (exploration, uncertainty reduction) and pragmatic (goal achievement) drives at the algorithmic and implementation levels. Proactive active inference is applicable to domains ranging from robotics, industrial automation, and digital twins to continual learning and neuroscience, where anticipation of novel outcomes and dynamic adaptation are required (Sedlak et al., 2023, Tschantz et al., 2019, Tschantz et al., 2020, Lanillos et al., 2021, Nuijten et al., 24 Nov 2025, Prakki, 2024, Daucé, 2017, Sajid et al., 2021, Torzoni et al., 17 Jun 2025, Watson et al., 2020, Çatal et al., 2020, Scholz et al., 2022, Shin et al., 2021).

1. Formalism: Expected Free Energy as the Proactive Objective

The core formalism posits that, for a generative model over latent states $s_{1:T}$ , observations $o_{1:T}$ , and policies $\pi$ , the expected free energy of a policy $\pi$ is

$G(\pi) = \mathbb{E}_{q(o_{1:T},s_{1:T}\mid\pi)} \left[ \ln q(s_{1:T}\mid\pi) - \ln \widetilde p(o_{1:T},s_{1:T} \mid \pi) \right].$

Expanding and time-decomposing for discrete-time partially observable Markov decision processes (POMDPs),

$G(\pi) = \sum_{\tau=1}^{T} \mathbb{E}_{q(o_\tau,s_\tau \mid \pi)} [ -\ln \tilde{p}(o_\tau) + \ln q(s_\tau \mid \pi) - \ln p(s_\tau) - \ln p(o_\tau \mid s_\tau) ],$

where $\tilde{p}(o_\tau)$ encodes prior preferences (pragmatic value), and the remaining terms comprise risk, ambiguity, and epistemic information gain (Nuijten et al., 24 Nov 2025, Sajid et al., 2021, Tschantz et al., 2020, Prakki, 2024, Lanillos et al., 2021, Torzoni et al., 17 Jun 2025). The objective functional $G(\pi)$ , minimized over possible future policies, enforces both trajectory-level exploitation and systematic, planned exploration.

2. Decomposition: Epistemic and Pragmatic Value

Expected free energy can be decomposed into components corresponding to epistemic value (exploration) and pragmatic value (goal-directedness): $G(\pi) = \underbrace{\mathbb{E}_{q(o_\tau \mid \pi)} [ -\ln \tilde{p}(o_\tau) ]}_{\text{Risk/Pragmatic}} + \underbrace{ \mathbb{E}_{q(s_\tau \mid \pi)} [ H[p(o_\tau \mid s_\tau)] ] }_{\text{Ambiguity}} - \underbrace{ I_q(O_\tau ; S_\tau \mid \pi)}_{\text{Epistemic gain}}.$

Pragmatic value (risk): Preference for obtaining observations $o_\tau$ with high prior probability under $\tilde{p}(o_\tau)$ , equivalent to utility or reward.
Ambiguity: Expected conditional entropy of observations given state; penalizes actions that yield unreliably predicted outcomes.
Epistemic value: Mutual information between hidden states and anticipated observations; proactive minimization systematically favors actions that reduce posterior uncertainty about the environment (Nuijten et al., 24 Nov 2025, Sajid et al., 2021, Tschantz et al., 2019, Tschantz et al., 2020).

This decomposition operationalizes the exploration–exploitation trade-off without introducing ad hoc bonuses or dual-mode heuristics. In the limit where prior preferences are flat, minimizing $G$ recovers optimal Bayesian experiment design; conversely, if ambiguity/epistemic terms vanish, $G$ recovers risk-sensitive expected utility maximization (Sajid et al., 2021).

3. Algorithmic Instantiations and Implementation Patterns

Sequential Action–Perception Cycle

A generic proactive active inference agent executes the following loop (Sedlak et al., 2023, Tschantz et al., 2019, Tschantz et al., 2020, Prakki, 2024, Lanillos et al., 2021, Scholz et al., 2022, Watson et al., 2020):

Belief Update: Receive $o_{t}$ , update $Q(s_{t})$ via variational free-energy minimization.
Policy Evaluation: For each candidate policy $\pi$ of length $H$ , simulate forward predictions under the generative model; compute $G(\pi)$ as above.
Action Selection: Choose $\pi^* = \arg\min_\pi G(\pi)$ ; execute the first action in $\pi^*$ .
Learning: Assimilate new data, update model parameters and CPTs.
Repeat.

Approximate inference machinery includes amortized variational inference (neural networks for q, p), cross-entropy methods (CEM) for high-dimensional policy optimization, forward Monte Carlo rollout, and local message passing schemes in factor graphs for scalability (Nuijten et al., 24 Nov 2025, Tschantz et al., 2019, Lanillos et al., 2021, Prakki, 2024).

Practical Details and Example

For discrete, low-dimensional models (e.g., smart factory testbed), all candidate actions can be enumerated explicitly, with explicit pragmatic, risk, and epistemic value calculation (Sedlak et al., 2023). In high-dimensional continuous control (e.g., deep RL or robotics), policies are sampled from a Gaussian or other tractable proposal, refined over iterations via CEM, and $G(\pi)$ is estimated through ensemble rollouts (Tschantz et al., 2019, Tschantz et al., 2020, Çatal et al., 2020, Lanillos et al., 2021).

Pseudocode for local message-passing in factored MDPs, which yields parallel updates for policy selection under EFE:

for each time t in 1..T:
    # Observation block
    q_{y, t} ← normalization[ p(y_t|x_t,θ) · r_{y|xθ,t} · goal_prior(y_t) · exp(−Λ_{xθ}) ]
    r_{y|xθ,t} ← normalize_over_y[ q_{y, t}/q_{sep, t} ]
    Λ_{xθ} ← -ln q_{sep,t} + ln ∫ p r exp(−λ_y) dy  + const
    # Dynamics block
    q_{dyn, t} ← normalization[ p(x_t|x_{t-1},θ,u_t) · goal_prior(x_t) · exp(−Λ_{xθ}−Λ_{trip}) ]
    Λ_{trip} ← ln q_{trip} - ln q_{pair} + const
    # Singleton consistency projections

(Nuijten et al., 24 Nov 2025)

4. Empirical Results and Applications

Industrial Edge Agents

In manufacturing, proactive active inference agents demonstrated rapid convergence to throughput-optimal, SLO-compliant parameters and traceable uncertainty reduction (Sedlak et al., 2023). Agents began from diverse initial states and converged to optimal operating points after just a few cycles, outperforming hand-tuned or naive feedback policies.

Model-based RL and Robotics

Active inference outperforms reward-only or random-exploration RL baselines in classic control and continuous-control benchmarks. Intrinsically-motivated exploration obtained via the epistemic term yields superior state-space coverage and sample efficiency ( $\sim$ 10× faster than DDPG in inverted pendulum and Hopper tasks) (Tschantz et al., 2019, Tschantz et al., 2020, Lanillos et al., 2021). In robotics, AIF agents generate human-like saccade policies in active vision, balance information-gathering with target pursuit, and solve sparse-reward navigation (MountainCar, Ant-Maze), with effective integration of deep representation learning and generative model-based planning (Lanillos et al., 2021, Daucé, 2017, Çatal et al., 2020, Scholz et al., 2022).

Continual Learning and Digital Twins

Proactive AIF supports robust adaptation and continual learning in nonstationary and partially-observed domains, as demonstrated in research agents for scientific hypothesis testing (Prakki, 2024) and digital twins for predictive maintenance (Torzoni et al., 17 Jun 2025). The addition of epistemic actions (e.g., explicit re-examination or remote sensing interventions) is essential for safety and rapid model adaptation in such applications.

5. Scalability, Approximations, and Implementation Challenges

aspect	Reactive AIF	Proactive AIF (EFE min)
Objective	F(x, u, o)	G(π) over horizon
Exploration	None	Intrinsic value (epistemic) drives
Planning depth	Local	Multi-step (T)
Computational cost	Low	$O(N \cdot T)$ , sampling/planning
Policy space	Greedy update	Horizon $H$ , combinatorial, approximated

(Lanillos et al., 2021)

Enumerative strategies: Feasible only for small, discrete spaces. For high-dimensional or continuous-control (e.g., robotics, industrial control), policy optimization employs cross-entropy, amortized variational autoencoders, or local message passing (Tschantz et al., 2019, Nuijten et al., 24 Nov 2025).
Local message passing: Provides polynomial—rather than exponential—scaling with planning horizon, and incorporates epistemic drive as entropic corrections to standard belief propagation (Nuijten et al., 24 Nov 2025).
Epistemic–pragmatic balancing: Direct calculation of mutual information terms is often intractable—approximations are necessary (Monte Carlo, mean-field, or Laplace approximations) (Tschantz et al., 2019, Çatal et al., 2020).
Model learning: Generative models and inference mechanisms must be updated online to cope with nonstationarity (e.g., drift, structural change), requiring robust continual learning and structure learning strategies (Sedlak et al., 2023, Prakki, 2024, Torzoni et al., 17 Jun 2025).
Computational limits: Proactive AIF demands more computation than reactive/incremental methods; scalable inference and planning, efficient function approximation for model parameters, and asynchronous/multiscale policy evaluation remain active areas (Lanillos et al., 2021, Nuijten et al., 24 Nov 2025).

6. Comparative Perspectives and Theoretical Significance

Relationship to RL: EFE minimization is mathematically equivalent to minimizing the negative value function in RL, but incorporates both epistemic and reward-seeking drives in a single variational bound (Shin et al., 2021, Nuijten et al., 24 Nov 2025, Tschantz et al., 2020). Standard RL approaches require ad hoc exploration bonuses or entropy regularization, while proactive AIF produces intrinsically-motivated exploration by design.
Control as Inference (CaI): Proactive AIF subsumes control-as-inference methods; policy inference with engineered “desired observations” is a special case of the EFE minimization framework (Watson et al., 2020).
Unified Planning-as-Inference: Recent work formalizes EFE minimization as a variational inference problem—policy selection is equivalent to minimizing a KL divergence against an unnormalized, EFE-weighted policy posterior (Nuijten et al., 24 Nov 2025), rendering epistemic drive as an explicit entropic effect in the objective and associated message-passing schemes.
Limiting Cases: When prior preferences are absent, proactive AIF reduces to pure information gain maximization (optimal experiment design). When ambiguity is minimized, it reduces to classical risk-sensitive expected utility (Sajid et al., 2021).

7. Limitations, Extensions, and Future Directions

Model Limitations: Restricted variable scopes, fixed cycle lengths, and lack of hierarchical generative modeling constrain application to real-world, nonstationary domains (Sedlak et al., 2023, Prakki, 2024).
Policy Search Complexity: Policy enumeration is intractable for large $|\mathcal{A}|$ , $T$ ; efficient planning, e.g., via hierarchical abstraction, variational message passing, or neural amortization, is required (Nuijten et al., 24 Nov 2025, Tschantz et al., 2019, Lanillos et al., 2021).
Cost of Epistemic Actions: Proactive exploration incurs real resource costs; balancing these against pragmatic drive is an emergent and unsolved problem (Sedlak et al., 2023, Torzoni et al., 17 Jun 2025).
Continual Learning and Adaptation: Continual adaptation to changing environments, structure learning for generative models, and hierarchical abstraction are critical for scalable deployment (Prakki, 2024, Torzoni et al., 17 Jun 2025, Nuijten et al., 24 Nov 2025).
Multi-agent and Distributed AIF: Coordination among multiple agents performing distributed free-energy minimization and maintenance of shared variational beliefs are significant open areas (Sedlak et al., 2023, Torzoni et al., 17 Jun 2025).
Unifying RL, Bayesian design, and inference: Proactive active inference continues to underpin a growing synthesis of foundational techniques in RL, Bayesian planning, and probabilistic inference (Nuijten et al., 24 Nov 2025, Shin et al., 2021, Tschantz et al., 2020, Sajid et al., 2021). Extensions to deep hierarchical agents, amortized planners, and real-time deployment are active research topics.