A Concise Mathematical Description of Active Inference in Discrete Time

In this paper we present a concise mathematical description of active inference in discrete time. The main part of the paper serves as a basic introduction to the topic, including a detailed example illustrating the theory on action selection. In the appendix the more subtle mathematical details are discussed. This part is aimed at readers who have already studied the active inference literature but struggle to make sense of the mathematical details and derivations. Throughout the whole manuscript, special attention has been paid to adopting notation that is both precise and in line with standard mathematical texts. All equations and derivations are linked to specific equation numbers in other popular text on the topic. Furthermore, Python code is provided that implements the action selection mechanism described in this paper and is compatible with pymdp environments.