Final Report Summary - DIRECTEDINFO (Investigating Directed Information)
The directed information is multi-letter expression (optimization over an infinite sum) and therefore very difficult to optimize or compute. Hence, we invented a new idea of graph-based auxiliary random variable that allows us to transform the multi-letter expression into a single letter convex optimization problem. Furthermore, in order to identify the structure of the graph-based auxiliary random variable we have introduced a reinforcement learning problem that its solution yields the desired structure. Right now these two novels ideas works well for finding the fundamental limits (capacity) of large families of finite state channel with feedback and we hope to develop these ideas for all problems where directed information plays an important role in communication and beyond.