An introduction to stochastic control theory, path integrals and reinforcement learning

Control theory is a mathematical description of how to act optimally to gain future rewards. In this paper I give an introduction to deterministic and stochastic control theory and I give an overview of the possible application of control theory to the modeling of animal behavior and learning. I discuss a class of non‐linear stochastic control problems that can be efficiently solved using a path integral or by MC sampling. In this control formalism the central concept of cost‐to‐go becomes a free energy and methods and concepts from statistical physics can be readily applied.