[Paper Review] Pedestrian crossing decisions can be explained by bounded optimal decision-making under noisy visual perception

Yueyang Wang, Aravinda Ramakrishnan Srinivasan+3 more|arXiv (Cornell University)|Feb 6, 2024

Impact of Light on Environment and HealthEnvironmental Science3 citations

TL;DR

This paper proposes a bounded optimal decision-making model for pedestrian crossing behavior, integrating noisy visual perception and reinforcement learning to explain gap acceptance and crossing timing. It demonstrates that behaviors previously viewed as cognitive biases—such as speed-dependent gap acceptance—are instead rational adaptations to perceptual constraints, outperforming prior models in replicating empirical phenomena.

ABSTRACT

This paper presents a model of pedestrian crossing decisions, based on the theory of computational rationality. It is assumed that crossing decisions are boundedly optimal, with bounds on optimality arising from human cognitive limitations. While previous models of pedestrian behaviour have been either 'black-box' machine learning models or mechanistic models with explicit assumptions about cognitive factors, we combine both approaches. Specifically, we model mechanistically noisy human visual perception and assumed rewards in crossing, but we use reinforcement learning to learn bounded optimal behaviour policy. The model reproduces a larger number of known empirical phenomena than previous models, in particular: (1) the effect of the time to arrival of an approaching vehicle on whether the pedestrian accepts the gap, the effect of the vehicle's speed on both (2) gap acceptance and (3) pedestrian timing of crossing in front of yielding vehicles, and (4) the effect on this crossing timing of the stopping distance of the yielding vehicle. Notably, our findings suggest that behaviours previously framed as 'biases' in decision-making, such as speed-dependent gap acceptance, might instead be a product of rational adaptation to the constraints of visual perception. Our approach also permits fitting the parameters of cognitive constraints and rewards per individual, to better account for individual differences. To conclude, by leveraging both RL and mechanistic modelling, our model offers novel insights about pedestrian behaviour, and may provide a useful foundation for more accurate and scalable pedestrian models.

Motivation & Objective

• To develop a computationally rational model of pedestrian crossing decisions that integrates cognitive constraints and environmental dynamics.
• To address the limitations of black-box ML models and overly simplistic mechanistic models in capturing individual variability and real-world complexity.
• To investigate whether behaviors traditionally labeled as 'biases' in pedestrian decision-making are instead rational responses to perceptual noise and cognitive limits.
• To improve model interpretability and scalability by combining mechanistic modeling of perception with reinforcement learning for policy optimization.
• To enable individual-level parameter fitting for better representation of diverse pedestrian behaviors.

Proposed method

• The model uses computational rationality, assuming pedestrians make boundedly optimal decisions under cognitive constraints such as noisy visual perception and motor delays.
• Visual perception is modeled as a noisy estimate of time-to-collision (TTA), with parameters for perceptual variance (σv) and looming aversion (c).
• A reinforcement learning (RL) framework learns the optimal policy for gap acceptance and crossing timing, conditioned on perceptual estimates and environmental parameters.
• The model incorporates motor delay (m) as a non-policy parameter to reflect the time lag between decision and action execution.
• Multiple model variants were tested: VLM (baseline), VLDM (with motor delay), VNM (alternative risk aversion formulation), VLM(E) (shared parameters), and VLM(S) (individual policies per parameter set).
• Model performance was evaluated using log-likelihood, AIC, and mean absolute deviation (MAD) against human behavioral data across constant-speed and yielding vehicle scenarios.

Figure 1: (a) Birds-eye view of the experiment. (b) A sample view of the virtual scene, as shown by the head-mounted display, at the beginning of each trial (inset) and as participants turned their heads to look for oncoming traffic. (Source: Pekkanen et al., 2021. Variable-drift diffusion models of

Experimental results

Research questions

• RQ1 Can pedestrian crossing decisions be explained by bounded optimal decision-making under noisy visual perception?
• RQ2 How do vehicle speed and stopping distance influence pedestrian gap acceptance and crossing timing?
• RQ3 Are behaviors like speed-dependent gap acceptance better explained as rational adaptations to perceptual noise rather than cognitive biases?
• RQ4 To what extent does incorporating motor delay and individualized perceptual parameters improve model fit and predictive accuracy?
• RQ5 How does the performance of a unified model (VLM) compare to individualized or alternative risk-aversion formulations (e.g., VLM(S), VNM) in replicating empirical pedestrian behavior?

Key findings

• The VLM model achieved the best balance of fit and complexity, with a log-likelihood of -536, AIC of 1192, and MAD of 0.35 seconds, outperforming all other variants.
• The inclusion of motor delay (VLDM) did not improve performance over VLM but increased model complexity, resulting in a higher AIC despite similar log-likelihood and MAD.
• The VLM(E) model, which used a single set of non-policy parameters across all participants, achieved a lower AIC (1098) than VLM but had worse log-likelihood, indicating that individualized parameters improve fit.
• The VLM(S) model, which trained separate RL policies for each parameter combination, did not improve performance over the original VLM, showing that parameter-conditioned policy learning is more efficient.
• The VNM model, which used proximity-based risk aversion instead of looming, showed higher MAD (0.99) and worse AIC, suggesting that temporal-spatial cues like looming are more critical than spatial proximity alone.
• The model successfully reproduced four key empirical phenomena: (1) gap acceptance dependence on TTA, (2) speed-dependent gap acceptance, (3) crossing timing in yielding scenarios, and (4) effect of vehicle stopping distance on crossing timing.

Figure 2: Comparison of models. (a) BM: Baseline Model. (b) LM: Looming aversion only. (c) VM: Visual limitation only. (d) VLM: Looming aversion and visual limitations. The abbreviations were introduced in Section 2.2 . $\sigma_{\mathrm{v}}$ and $c$ represent the sensory noise and looming aversion w