  An open question in autonomous driving is how best to use simulation to
validate the safety of autonomous vehicles. Existing techniques rely on
simulated rollouts, which can be inefficient for finding rare failure events,
while other techniques are designed to only discover a single failure. In this
work, we present a new safety validation approach that attempts to estimate the
distribution over failures of an autonomous policy using approximate dynamic
programming. Knowledge of this distribution allows for the efficient discovery
of many failure examples. To address the problem of scalability, we decompose
complex driving scenarios into subproblems consisting of only the ego vehicle
and one other vehicle. These subproblems can be solved with approximate dynamic
programming and their solutions are recombined to approximate the solution to
the full scenario. We apply our approach to a simple two-vehicle scenario to
demonstrate the technique as well as a more complex five-vehicle scenario to
demonstrate scalability. In both experiments, we observed an increase in the
number of failures discovered compared to baseline approaches.
