Reach-avoid sets are used in robotics to identify states from which a robot can complete a task while staying safe. Classical methods such as Hamilton-Jacobi reachability treat disturbances as adversarial, assuming the worst-case within a bounded set. That guarantees safety but can be overly conservative when disturbances are actually random.
The authors propose a probabilistic reach-avoid value function (PVF) learned via temporal difference methods. It is self-supervised and does not require a model of the system, making it applicable to black-box systems. The method handles stochastic, potentially unbounded disturbances and estimates the probability that a state leads to success while avoiding unsafe regions.
The authors evaluated PVF against HJR-based baselines on systems of increasing complexity, up to a Hopper locomotion task. When disturbances were non-adversarial, the probabilistic sets were less conservative and more accurate than the adversarial HJR sets, suggesting a practical trade-off between worst-case guarantees and task feasibility.