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

TL;DR

A model of pedestrian crossing decisions, based on the theory of computational rationality, is presented, suggesting 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.

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.

Figures (14)

• 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 pedestrian road-crossing decisions. Computational Brain $\&$ Behavior, 1–21. This image is available under a Creative Commons Attribution 4.0 International License.)
• 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 \ref{['subsec:Main Model variants']}. $\sigma_\mathrm{v}$ and $c$ represent the sensory noise and looming aversion weight respectively. $s$, $o$, $a$, and $r$ represent the state, observation, action and reward respectively.
• Figure 3: Empirical results. (a) Gap acceptance rate in constant-speed scenarios. (b) Cumulative probability of Crossing Initiation Time (CIT) in constant-speed scenarios; black dashed vertical lines indicate the times vehicles passed pedestrians. The X-axis means the time elapsed from the beginning of each trial. (c) Cumulative probability of CIT in yielding scenarios. Note: In yielding scenarios, there are only two conditions in the initial TTA of 6.9 s as shown in \ref{['tab:scenarios']}, so there is no gray line in the third panel of yielding scenarios.
• Figure 4: Gap acceptance rate by human participants and different models. BM: Baseline model. LM: Model with the looming aversion assumption. VM: Model with the visual limitation assumption. VLM: Model with both visual limitation and looming aversion assumptions. Note: the lines of the model LM and BM overlap each other.
• Figure 5: Cumulative probability for Crossing Initiation Time (CIT) in constant-speed scenarios. Black dashed vertical lines in Human data indicate the times vehicles passed pedestrians. To avoid repetition, these grey lines are not included in the model results. Vehicles passed pedestrians at the same time in the trial for each initial TTA condition. The X-axis means the time elapsed from the beginning of each trial. The KS statistic quantifies the maximum divergence between the cumulative distribution functions of human data and model results, indicating their distributional similarity. Model abbreviations are as defined in \ref{['fig:GapPlot']}.