  Reinforcement learning algorithms describe how an agent can learn an optimal
action policy in a sequential decision process, through repeated experience. In
a given environment, the agent policy provides him some running and terminal
rewards. As in online learning, the agent learns sequentially. As in
multi-armed bandit problems, when an agent picks an action, he can not infer
ex-post the rewards induced by other action choices. In reinforcement learning,
his actions have consequences: they influence not only rewards, but also future
states of the world. The goal of reinforcement learning is to find an optimal
policy -- a mapping from the states of the world to the set of actions, in
order to maximize cumulative reward, which is a long term strategy. Exploring
might be sub-optimal on a short-term horizon but could lead to optimal
long-term ones. Many problems of optimal control, popular in economics for more
than forty years, can be expressed in the reinforcement learning framework, and
recent advances in computational science, provided in particular by deep
learning algorithms, can be used by economists in order to solve complex
behavioral problems. In this article, we propose a state-of-the-art of
reinforcement learning techniques, and present applications in economics, game
theory, operation research and finance.
