Emotion in an active inference model of human driving

Technical Summary: Emotion in an Active Inference Model of Human Driving

Problem Statement
Active inference has emerged as a principled framework for modeling adaptive behavior by balancing goal-directed action with uncertainty reduction. While successfully applied to human driving scenarios (e.g., car-following, lane-keeping, collision avoidance), existing models largely neglect affective state (emotion), a critical determinant of human decision-making in traffic. Previous attempts to integrate emotions into active inference have been limited to simplified, discrete state-space "toy problems" that lack the capacity for realistic planning required in complex traffic scenarios. There is a need to extend these emotional modeling capabilities to continuous state-space models of driving that account for multi-step policy planning.

Methodology
The authors extend an existing active inference model of human driving collision avoidance (Schumann et al.) to incorporate a model of driver emotion based on Russell's circumplex model of affect (valence and arousal). The core framework operates as follows:

1. Generative Model: The agent maintains a stochastic belief $q(s)$ (via particle filters) about the environment, approximating an external generative process. The transition model combines a kinematic likelihood (bicycle model) and a normative likelihood (compliance with traffic rules).
2. Policy Selection: The agent evaluates candidate policies $\pi_t$ (sequences of actions over a horizon $H$) by minimizing Expected Free Energy (EFE). EFE balances pragmatic value (achieving preferred outcomes) and epistemic value (reducing uncertainty).
3. Emotion Formulation:
   • Valence ($V$): Defined as the difference between actual and expected pragmatic value. To adapt this to continuous time and multi-step planning, the authors propose:
     • Dividing by the time step $\Delta t$ to ensure frequency independence.
     • Calculating Expected Value ($V(E)$) as the average pragmatic value over the predicted states of the previous $N=5$ policies to ensure stability against stochastic policy selection.
     • Calculating Actual Value ($V(A)$) based on the current reference policy (the one currently in effect) rather than counterfactuals, reflecting ongoing organism-environment interactions.
     • $V_t = V(A)_t - V(E)_t$.
   • Arousal ($A$): Defined as the entropy of the agent's posterior belief. The authors argue that using raw kinematic uncertainty is counterintuitive (e.g., distant agents might induce high uncertainty/arousal while imminent collisions might induce low uncertainty due to precise tracking). Instead, they map arousal to the uncertainty of a meaningful abstract state: the probability of collision ($p_{coll}$).
     • $p_{coll}$ is the expected maximum probability of collision over the prediction horizon, derived from a binary collision classifier.
     • Arousal is calculated as the binary entropy of this collision probability: $A_t = -[p_{coll} \ln(p_{coll}) + (1-p_{coll}) \ln(1-p_{coll})]$.

Key Contributions

• Continuous State Extension: The paper generalizes the discrete-state emotion formulation of Pattisapu et al. to a continuous state-space active inference model of driving.
• Future-Oriented Appraisal: The proposed formulation conditions affective estimates not only on current states but also on predicted future outcomes (over a multi-step horizon), aligning with appraisal theories of emotion.
• Stable Valence Estimation: By averaging expected values over multiple past policies, the model reduces variability caused by stochastic policy selection, yielding more stable affective signals.
• Semantic Arousal: The authors introduce a method to derive arousal from the uncertainty of high-level semantic states (collision likelihood) rather than low-level kinematic uncertainty, avoiding irrational arousal responses to distant, non-threatening agents.

Results
The approach was evaluated in two interactive driving scenarios involving 128 simulations each: a lateral incursion scenario and an intersection with priority violation. The agent interacted with either a compliant or a non-compliant (adversarial) agent.

• Lateral Incursion:
  • Compliant Agent: Arousal increased initially as collision likelihood rose but decreased as the other agent behaved benignly. Valence became positive as the pragmatic value improved.
  • Non-Compliant Agent: Upon the other agent violating norms, the modeled agent lost trust, leading to increased uncertainty (arousal) and negative valence. The agent successfully avoided a collision, causing a subsequent drop in arousal and rise in valence.
• Intersection:
  • Compliant Agent: Emotions remained neutral/calm as the other agent yielded.
  • Non-Compliant Agent: The agent experienced negative valence and increased arousal as the other agent ignored traffic rules. In successful avoidance cases, the agent yielded, leading to relief (positive valence). In collision cases, arousal decreased only when the collision became unavoidable (certainty of outcome), and valence remained lower than in avoidance cases.
• Circumplex Mapping: When mapped to the circumplex model, the agent's emotional states aligned with human patterns: norm violations induced anger (negative valence, high arousal), while successful avoidance led to relaxation. Collision outcomes transitioned from sadness to depression.

Significance and Claims
The paper claims that active inference provides a viable and principled framework for modeling the affective components of human driving behavior. The primary significance lies in:

1. Mechanistic Interpretability: The model offers a structured explanation for how emotional states arise from cognitive processes (e.g., deviations from expected outcomes induce negative valence; uncertainty about norm violations induces arousal).
2. Alignment with Appraisal Theory: The results support appraisal theories by demonstrating that affective responses are driven by anticipated outcomes and the violation of social/normative expectations.
3. Unified Framework: The work supports the view of active inference as a unified account of perception, action, and affect, showing that affective states can be inferred from the same generative framework used for behavior modeling.

Limitations
The authors note several limitations:

• The model captures short-term prediction errors but neglects higher-level or long-term expectations (e.g., a driver in a traffic jam may still feel negative valence despite stable short-term predictions).
• The evaluation is limited to simulation; no direct comparison with human data (e.g., facial expressions) has been performed.
• The model is unidirectional (behavior affects emotion) and does not yet account for how emotions might modulate behavior (e.g., anger increasing risk-taking).