  We consider a sequential decision making problem where the agent faces the
environment characterized by the stochastic discrete events and seeks an
optimal intervention policy such that its long-term reward is maximized. This
problem exists ubiquitously in social media, finance and health informatics but
is rarely investigated by the conventional research in reinforcement learning.
To this end, we present a novel framework of the model-based reinforcement
learning where the agent's actions and observations are asynchronous stochastic
discrete events occurring in continuous-time. We model the dynamics of the
environment by Hawkes process with external intervention control term and
develop an algorithm to embed such process in the Bellman equation which guides
the direction of the value gradient. We demonstrate the superiority of our
method in both synthetic simulator and real-world problem.
