  Safety performance evaluation is critical for developing and deploying
connected and automated vehicles (CAVs). One prevailing way is to design
testing scenarios using prior knowledge of CAVs, test CAVs in these scenarios,
and then evaluate their safety performances. However, significant differences
between CAVs and prior knowledge could severely reduce the evaluation
efficiency. Towards addressing this issue, most existing studies focus on the
adaptive design of testing scenarios during the CAV testing process, but so far
they cannot be applied to high-dimensional scenarios. In this paper, we focus
on the adaptive safety performance evaluation by leveraging the testing
results, after the CAV testing process. It can significantly improve the
evaluation efficiency and be applied to high-dimensional scenarios.
Specifically, instead of directly evaluating the unknown quantity (e.g., crash
rates) of CAV safety performances, we evaluate the differences between the
unknown quantity and known quantity (i.e., control variates). By leveraging the
testing results, the control variates could be well designed and optimized such
that the differences are close to zero, so the evaluation variance could be
dramatically reduced for different CAVs. To handle the high-dimensional
scenarios, we propose the sparse control variates method, where the control
variates are designed only for the sparse and critical variables of scenarios.
According to the number of critical variables in each scenario, the control
variates are stratified into strata and optimized within each stratum using
multiple linear regression techniques. We justify the proposed method's
effectiveness by rigorous theoretical analysis and empirical study of
high-dimensional overtaking scenarios.
