Optimistic Monte Carlo Tree Search with Sampled Information Relaxation Dual Bounds.

In the paper, "Optimistic Monte Carlo Tree Search with Sampled Information Relaxation Dual Bounds," the authors propose an extension to Monte Carlo tree search that uses the idea of "sampling the future" to produce noisy upper bounds on nodes in the decision tree. These upper bounds can help guide the tree expansion process and produce decision trees that are deeper rather than wider, in effect concentrating computation toward more useful parts of the state space. The algorithm's effectiveness is illustrated in a ride-sharing setting, where a driver/vehicle needs to make dynamic decisions regarding trip acceptance and relocations. 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 toward 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 "optimistic" tree search technique called primal-dual MCTS that uses sampled information relaxation upper bounds on potential actions to make tree expansion decisions, creating the possibility of ignoring parts of the tree that stem from highly suboptimal choices. The core contribution of this paper is to prove that despite converging to a partial decision tree in the limit, the recommended action from primal-dual MCTS is optimal. The new approach shows promise when used to optimize the behavior of a single driver navigating a graph while operating on a ride-sharing platform. Numerical experiments on a real data set of taxi trips in New Jersey suggest that primal-dual MCTS improves on standard MCTS (upper confidence trees) and other policies while exhibiting a reduced sensitivity to the size of the action space. [ABSTRACT FROM AUTHOR]