Connecting Stochastic Optimal Control and Reinforcement Learning

In this article we study the connection of stochastic optimal control and reinforcement learning. Our main motivation is an importance sampling application to rare events sampling which can be reformulated as an optimal control problem. By using a parameterized approach the optimal control problem turns into a stochastic optimization problem which still presents some open questions regarding how to tackle the scalability to high-dimensional problems and how to deal with the intrinsic metastability of the system. With the aim to explore new methods we connect the optimal control problem to reinforcement learning since both share the same underlying framework namely a Markov decision process (MDP). We show how the MDP can be formulated for the optimal control problem. Furthermore, we discuss how the stochastic optimal control problem can be interpreted in a reinforcement learning framework. At the end of the article we present the application of two different reinforcement learning algorithms to the optimal control problem and compare the advantages and disadvantages of the two algorithms