Model-Based Performance Evaluation of Safety-Critical POMDPs

Partially Observable Markov Decision Processes (POMDPs) have been successfully employed for planning and control in safety-critical applications (e.g., autonomous vehicles) with uncertain environments. POMDP development is a subjective process and depends on assumptions inferred from available information from system-environment interactions. This subjective process can result in different designs (e.g., different state-spaces) where one needs to analyze their performance and robustness to choose the POMDP that best satisfies safety and performance requirements. The robustness and performance depend on accurately inferring states and providing optimal and safe responses in presence of uncertainties, such that the goal can be achieved without violating safety requirements. These properties are typically evaluated by extensive, end-to-end testing of the developed POMDPs in simulated environments and measuring their average performance in simulated scenarios, where the measured performance relies entirely on the end results (e.g., crash or no crash) obtained from the simulated scenarios. To avoid this suboptimal process, we propose a model-based, probabilistic technique to evaluate performance and robustness of a class of POMDPs, where states are designed to represent various high-level situations in the environment, including both the goal and failure states. In this technique, the robustness and performance of designed POMDPs are evaluated by mapping POMDPs to their belief-space and estimating the extreme and expected probability of transitioning to failure states. Finally, we employ our technique to compare and evaluate two different POMDPs designed for controlling an AV in a safety-critical use-case scenario (lane-keeping with risky situations and corner-cases). By comparing the results obtained from our technique to end-to-end simulation-based evaluation, we show that the proposed technique can correctly identify the POMDP with best performance.