Policy learning for time-bounded reachability in continuous-time Markov decision processes via doubly-stochastic gradient ascent

Continuous-time Markov decision processes are an important class of models in a wide range of applications, ranging from cyber-physical systems to synthetic biology. A central problem is how to devise a policy to control the system in order to maximise the probability of satisfying a set of temporal logic specifications. Here we present a novel approach based on statistical model checking and an unbiased estimation of a functional gradient in the space of possible policies. The statistical approach has several advantages over conventional approaches based on uniformisation, as it can also be applied when the model is replaced by a black box, and does not suffer from state-space explosion. The use of a stochastic gradient to guide our search considerably improves the efficiency of learning policies. We demonstrate the method on a proof-of-principle non-linear population model, showing strong performance in a non-trivial task.