A Counterfactual Safety Margin Perspective on the Scoring of Autonomous Vehicles' Riskiness

Autonomous Vehicles (AVs) have the potential to provide numerous societal benefits, such as decreased road accidents and increased overall transportation efficiency. However, quantifying the risk associated with AVs is challenging due to the lack of historical data and the rapidly evolving technology. This paper presents a data-driven framework for comparing the risk of different AVs' behaviors in various operational design domains (ODDs), based on counterfactual simulations of "misbehaving" road users. We introduce the concept of counterfactual safety margin, which represents the minimum deviation from normal behavior that could lead to a collision. This concept helps to find the most critical scenarios but also to assess the frequency and severity of risk of AVs. We show that the proposed methodology is applicable even when the AV's behavioral policy is unknown -- through worst- and best-case analyses -- making the method useful also to external third-party risk assessors. Our experimental results demonstrate the correlation between the safety margin, the driving policy quality, and the ODD shedding light on the relative risk associated with different AV providers. This work contributes to AV safety assessment and aids in addressing legislative and insurance concerns surrounding this emerging technology.

Factorization of Multi-Agent Sampling-Based Motion Planning

Modern robotics often involves multiple embodied agents operating within a shared environment. Path planning in these cases is considerably more challenging than in single-agent scenarios. Although standard Sampling-based Algorithms (SBAs) can be used to search for solutions in the robots' joint space, this approach quickly becomes computationally intractable as the number of agents increases. To address this issue, we integrate the concept of factorization into sampling-based algorithms, which requires only minimal modifications to existing methods. During the search for a solution we can decouple (i.e., factorize) different subsets of agents into independent lower-dimensional search spaces once we certify that their future solutions will be independent of each other using a factorization heuristic. Consequently, we progressively construct a lean hypergraph where certain (hyper-)edges split the agents to independent subgraphs. In the best case, this approach can reduce the growth in dimensionality of the search space from exponential to linear in the number of agents. On average, fewer samples are needed to find high-quality solutions while preserving the optimality, completeness, and anytime properties of SBAs. We present a general implementation of a factorized SBA, derive an analytical gain in terms of sample complexity for PRM*, and showcase empirical results for RRG.

How Bad is Selfish Driving? Bounding the Inefficiency of Equilibria in Urban Driving Games

We consider the interaction among agents engaging in a driving task and we model it as general-sum game. This class of games exhibits a plurality of different equilibria posing the issue of equilibrium selection. While selecting the most efficient equilibrium (in term of social cost) is often impractical from a computational standpoint, in this work we study the (in)efficiency of any equilibrium players might agree to play. More specifically, we bound the equilibrium inefficiency by modeling driving games as particular type of congestion games over spatio-temporal resources. We obtain novel guarantees that refine existing bounds on the Price of Anarchy (PoA) as a function of problem-dependent game parameters. For instance, the relative trade-off between proximity costs and personal objectives such as comfort and progress. Although the obtained guarantees concern open-loop trajectories, we observe efficient equilibria even when agents employ closed-loop policies trained via decentralized multi-agent reinforcement learning.

Posetal Games: Efficiency, Existence, and Refinement of Equilibria in Games with Prioritized Metrics

Modern applications require robots to comply with multiple, often conflicting rules and to interact with the other agents. We present Posetal Games as a class of games in which each player expresses a preference over the outcomes via a partially ordered set of metrics. This allows one to combine hierarchical priorities of each player with the interactive nature of the environment. By contextualizing standard game theoretical notions, we provide two sufficient conditions on the preference of the players to prove existence of pure Nash Equilibria in finite action sets. Moreover, we define formal operations on the preference structures and link them to a refinement of the game solutions, showing how the set of equilibria can be systematically shrunk. The presented results are showcased in a driving game where autonomous vehicles select from a finite set of trajectories. The results demonstrate the interpretability of results in terms of minimum-rank-violation for each player.