Piecewise-deterministic Markov processes (PDMPs) are a class of stochastic models with deterministic dynamics punctuated by discrete random jumps. In this talk, we use PDMPs to study optimal path planning in an environment where random jumps can impact the optimization objective. We investigate what happens if a planner does not immediately know when a stochastic jump has occurred, but instead may obtain infrequent observations of the environment’s current operating mode. We consider multiple observation schemes, present a numerical approach for efficiently computing optimal policies in these scenarios, and look at examples motivated by minimizing exposure to surveillance while traveling.
Joint work with Alex Vladimirsky, building on preliminary results obtained with REU students Natasha Patnaik and Naga Rudrapatna.