Automated Vehicle Safety Evaluation with Aggregate Markov Chain and Constraint Transfer Learning

Abstract: Automated vehicle (AV) safety evaluation requires the assessment of the occurrence and evolution of safety-critical rare states. Existing scenario-based methods rely on designed episodes of limited duration to estimate accident rates, but they fail to account for how vehicles transition into dangerous states over time. This paper introduces a new perspective that analyzes the occurrence probabilities of states of interest over an infinite driving process, providing a comprehensive examination of the distribution and evolution of near-collision states. By applying Markov Chain steady-state probability theory, state probability distributions are derived from state transition matrices, which can be directly extracted from AV action models, thus circumventing the "curse of rarity." To address the challenge posed by high-dimensional state spaces, we introduce aggregate Markov Chain theory to cluster the state space for more efficient estimation. This approach aggregates microscopic states into macroscopic blocks, simplifying the complex microscopic state transitions into macroscopic block transition probability estimation, thereby reducing computational complexity.

To estimate transition probabilities across states, we first express the transition probabilities as a function of state occurrence probabilities. Subsequently, we propose a Constraint Transfer Learning approach to predict the occurrence probabilities of individual states. Specifically, we introduce a mechanism that leverages the mapping relationships between parent and child states in a Markov Chain to constrain the training of the network. By incorporating transfer learning methods, the predictive network is designed to estimate the occurrence probabilities of dangerous states from safe state data.

Simulation experiments compare the proposed method with the Monte Carlo benchmark, demonstrating that the proposed approach can estimate dangerous state probabilities using a small sample size while providing more insightful safety assessments than existing methods.