I am looking for a reference that would provide a formal definition of a decision tree. I am mostly referring to combinatorial games, Markov decision processes and similar fields. It should be something more or less like:
- Let A be the set of actions that a player could take, then the decision tree is the free monoid A*
or maybe
- Let G=(V,E) be a digraph such that V is the set of states of the game and edges E connecting states $(v_1,v_2)\in E$ if player can transition from $v_1$ to $v_2$ in one step. Edges may be labelled with their respective actions.
Strangely I can't find any book/paper that would actually provide the formal definition. The entire "Reinforcement Learning" by Barto & Sutton does not actually define it. I need something to reference. If you know of some large book, please mention the page.
