Feature selection as Monte-Carlo Search in Growing Single Rooted Directed Acyclic Graph by Best Leaf Identification

Monte Carlo tree search (MCTS) has received considerable interest due to its spectacular success in the difficult problem of computer Go and also proved beneficial in a range of other domains. A major issue that has received little attention in the MCTS literature is the fact that, in most games, different actions can lead to the same state, that may lead to a high degree of redundancy in tree representation and unnecessary additional computational cost. We extend MCTS to single rooted directed acyclic graph (SR-DAG), and consider the Best Arm Identification (BAI) and the Best Leaf Identification (BLI) problem of an expanding SR-DAG of arbitrary depth. We propose algorithms that are (epsilon, delta)-correct in the fixed confidence setting, and prove an asymptotic upper bounds of sample complexity for our BAI algorithm. As a major application for our BLI algorithm, a novel approach for Feature Selection is proposed by representing the feature set space as a SR-DAG and repeatedly evaluating feature subsets until a candidate for the best leaf is returned, a proof of concept is shown on benchmark data sets.