Feasible Action Space Reduction for Quantifying Causal Responsibility in Continuous Spatial Interactions

TL;DR

Feasible Action-Space Reduction (FeAR) extends causal-responsibility quantification from discrete to continuous action spaces in spatial interactions by defining feasible action spaces, their hypervolumes, and a normative Move de Rigueur (MdR) for counterfactual comparisons. The framework yields FeAR values that indicate when an agent is assertive or courteous, and enables backward-looking assessments of responsibility as well as forward-looking, responsibility-aware action selection. Through prototypical space-sharing case studies, the paper demonstrates how FeAR captures inter-agent influence, the impact of environmental constraints, and the role of normative expectations on responsibility. This approach provides a model-agnostic, graded measure of causal responsibility with potential to inform safe and accountable navigation in human-robot and mixed-traffic settings, while highlighting areas for real-time deployment and extension to groups and non-holonomic dynamics.

Abstract

Understanding the causal influence of one agent on another agent is crucial for safely deploying artificially intelligent systems such as automated vehicles and mobile robots into human-inhabited environments. Existing models of causal responsibility deal with simplified abstractions of scenarios with discrete actions, thus, limiting real-world use when understanding responsibility in spatial interactions. Based on the assumption that spatially interacting agents are embedded in a scene and must follow an action at each instant, Feasible Action-Space Reduction (FeAR) was proposed as a metric for causal responsibility in a grid-world setting with discrete actions. Since real-world interactions involve continuous action spaces, this paper proposes a formulation of the FeAR metric for measuring causal responsibility in space-continuous interactions. We illustrate the utility of the metric in prototypical space-sharing conflicts, and showcase its applications for analysing backward-looking responsibility and in estimating forward-looking responsibility to guide agent decision making. Our results highlight the potential of the FeAR metric for designing and engineering artificial agents, as well as for assessing the responsibility of agents around humans.

Figures (8)

• Figure 1: Representing a spatial interaction --- (a) a space-sharing interaction where agent 1 (the robot, grey) cuts off agent 2 (the human, pink) while doing a U-Turn; (b) constant acceleration trajectories $\widehat{\tau_{i}}$ of the agents at each time step within a time window $[0, T]$. The starting locations of agents $(x_{i}(0), y_{i}(0))$ are indicated by the black outlines, and the initial velocities of agents $(v_{x,i}(0), v_{y,i}(0))$ are indicated by the lengths of the arrows; (c) convex hulls of the bounding boxes at the start ($t$) and end ($t+ \delta t$) of time intervals $\Delta T_t = [t, t+\delta t]$. These hulls are used to check for collisions with obstacles or other agents, and subsequently compute the trajectories of agents $\tau_{i}$, where agents stop moving after collisions. Thus, $\tau_{i}$ captures how other agents or obstacles might be influencing the location, velocity and collision state of agent $i$.
• Figure 2: Computing the Feasible Action Space for one agent. We divide the action space of an agent into subsets and mark an action subset as feasible (blue) if all the actions within that subset lead to feasible trajectories. Two consecutive time intervals without and with collisions are shown in (a). Action subsets leading to collisions are marked infeasible (red) in the final configuration space and action space plots (b).
• Figure 3: Calculating FeAR: In a given scenario, to ascertain causal responsibility, we compare the actions performed by agents (a) with the expected moves de rigueur (MdR) of the agents (b), and calculate the FeAR values (d) based on the feasible action spaces shown in (c), by comparing the hypervolumes of the feasible action spaces $\mathcal{V}_{j} \bigl(S, A \bigr)$ and $\mathcal{V}_{j} \bigl(S, \left[ A_{i} \leftarrow \mu_{i} \right] \bigr)$ as shown in (e). $\mathrm{FeAR}_{i,j \neq i}$ represent the causal responsibility of agent $i$ on the trajectory $\tau_{j}$ of agent $j$. $\mathrm{FeAR}_{i,i}$ (the diagonal elements which are highlighted) represents how all the other agents $\neg i$ affect the causal responsibility of agent $i$ for its own trajectory $\tau_{i}$.
• Figure 4: Properties of the FeAR metric in prototypical space-sharing conflicts: These case studies illustrate the properties of FeAR when applied to prototypical space sharing conflicts. $\mathrm{FeAR}_{i,j}>0$ indicates that agent $i$ is being assertive towards agent $j$, and courteous if $\mathrm{FeAR}_{i,j}<0$. In all these case studies we assume that the move de rigueur for all the agents is to keep moving in their current direction with the current speed (i.e., have zero acceleration).
• Figure 5: The effect of Move de Rigueur on FeAR: Different contexts might warrant different expectations for the actions of agents. In the interaction of one agent going head-on towards two other agents, different joint actions $A$ (rows) and different choices of MdR $\mu$ (columns) lead to different FeAR values. For brevity, only four most informative FeAR values are shown for each case. Denoting the vertical position of the agent as $y$, and the attraction to the center of the lane as $k_{\text{lane}}$, the joint actions/MdRs are defined as: