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Continuous-time Markov decision processes are an important class of models ina wide range of applications, ranging from cyber-physical systems to syntheticbiology. A central problem is how to devise a policy to control the system inorder to maximise the probability of satisfying a set of temporal logicspecifications. Here we present a novel approach based on statistical modelchecking and an unbiased estimation of a functional gradient in the space ofpossible policies. The statistical approach has several advantages overconventional approaches based on uniformisation, as it can also be applied whenthe model is replaced by a black box, and does not suffer from state-spaceexplosion. The use of a stochastic gradient to guide our search considerablyimproves the efficiency of learning policies. We demonstrate the method on aproof-of-principle non-linear population model, showing strong performance in anon-trivial task.

Policy learning for time-bounded reachability in Continuous-Time Markov Decision Processes via doubly-stochastic gradient ascent