Monte Carlo Tree Search (MCTS), most famously used in game-play artificial intelligence (e.g., the game of Go), is a well-known strategy for constructing approximate solutions to sequential decision problems. Its primary innovation is the use of a heuristic, known as a default policy, to obtain Monte Carlo estimates of downstream values for states in a decision tree. This information is used to iteratively expand the tree towards regions of states and actions that an optimal policy might visit. However, to guarantee convergence to the optimal action, MCTS requires the entire tree to be expanded asymptotically. In this paper, we propose a new technique called Primal-Dual MCTS that utilizes sampled information relaxation upper bounds on potential actions, creating the possibility of "ignoring" parts of the tree that stem from highly suboptimal choices. This allows us to prove that despite converging to a partial decision tree in the limit, the recommended action from Primal-Dual MCTS is 查看全文>>