UCD : Upper confidence bound for rooted directed acyclic graphs

In this paper we present a framework for testing various algorithms that deal with transpositions in Monte-Carlo Tree Search (MCTS). We call this framework Upper Confidence bound for Direct acyclic graphs (UCD) as it constitutes an extension of Upper Confidence bound for Trees (UCT) for Direct acyclic graphs (DAG).When using transpositions in MCTS, a DAG is progressively developed instead of a tree. There are multiple ways to handle the exploration exploitation dilemma when dealing with transpositions. We propose parameterized ways to compute the mean of the child, the playouts of the parent and the playouts of the child. We test the resulting algorithms on several games. For all games, original configurations of our algorithms improve on state of the art algorithms.