Monte Carlo Tree Search Sample Clauses

Monte Carlo Tree Search. Recently, Monte Carlo Tree Search has been shown to yield good quality Xxxxxx schemes [53]. We will describe its characteristics, so that we can see if we can improve its performance. Monte Carlo Tree Search (MCTS) is a tree search method that has been successful in games such as Go, Hex, and other applications with a large state space [65, 66]. It works by selectively building a tree, expanding only branches it deems worthwhile to explore. MCTS consists of four steps, which are displayed in figure 3. The first step (3a) is the selection step, where a leaf or a not fully expanded node is selected according to some criterion (see below). Our choice is node z. In the expansion step (3b), a random unexplored child of the selected node is added to the tree (node y). In the simulation step (3(c)), the rest of the path to a final node is completed using random child selection. Finally a score ∆ is obtained that signifies the score of the chosen path through the state space. In the backpropagation step (3d), this value is propagated back through the tree, which affects the average score (winrate) of a node (see below). The tree is built iteratively by repeating the four steps. In the game of Go, each node represents a player move and in the expansion phase the game is played out, in basic implementations, by random moves. In the best performing implementations heuristics and pattern knowledge are used to complement a random playout [65]. The final score is 1 if the game is won, and 0 if the game is lost. The entire tree is built, ultimately, to select the best first move. For our purposes, we need to build a complete Xxxxxx scheme, variable by variable. As such, each node will represent a variable and the depth of a node in the tree represents the position in the Xxxxxx scheme. Thus, in figure 3(c) the partial Xxxxxx scheme is x,z,y and the rest of the scheme is filled in randomly with unused variables. The score of a path in our case, is the improvement of the path on the number of operations: the original number of operations divided by the number of operations after the Xxxxxx scheme and CSEE have been applied. We note that for our purposes the entire Xxxxxx scheme is important and not just the first variable. a. b. c. d. x z w x z w y ∆ ∆ ∆ ∆ x z

Monte Carlo Tree Search