Guarantees on Robot System Performance Using Stochastic Simulation Rollouts

In this article, we provide finite-sample performance guarantees for control policies executed on stochastic robotic systems. Given an open- or closed-loop policy and a finite set of trajectory rollouts under the policy, we bound the expected value, value at risk, and conditional value at risk of the trajectory cost, and the probability of failure in a sparse cost setting. The bounds hold, with user-specified probability, for any policy synthesis technique and can be seen as a postdesign safety certification. Generating the bounds only requires sampling simulation rollouts, without assumptions on the distribution or complexity of the underlying stochastic system. We adapt these bounds to also give a constraint satisfaction test to verify the safety of the robot system. We provide a thorough analysis of the bound sensitivity to sim-to-real distribution shifts and provide results for constructing robust bounds that can tolerate some specified amount of distribution shift. Furthermore, we extend our method to apply when selecting the best policy from a set of candidates, requiring a multihypothesis correction. We show the statistical validity of our bounds in the Ant, Half-cheetah, and Swimmer MuJoCo environments and demonstrate our constraint satisfaction test with the Ant. Finally, using the 20-degree-of-freedom MuJoCo Shadow Hand, we show the necessity of the multihypothesis correction.