Dynamic Non-Bayesian Decision Making

The model of a non-Bayesian agent who faces a repeated game with incomplete information against Nature is an appropriate tool for modeling general agent-environment interactions. In such a model the environment state (controlled by Nature) may change arbitrarily, and the feedback/reward function is initially unknown. The agent is not Bayesian, that is he does not form a prior probability neither on the state selection strategy of Nature, nor on his reward function. A policy for the agent is a function which assigns an action to every history of observations and actions. Two basic feedback structures are considered. In one of them -- the perfect monitoring case -- the agent is able to observe the previous environment state as part of his feedback, while in the other -- the imperfect monitoring case -- all that is available to the agent is the reward obtained. Both of these settings refer to partially observable processes, where the current environment state is unknown. Our main result refers to the competitive ratio criterion in the perfect monitoring case. We prove the existence of an efficient stochastic policy that ensures that the competitive ratio is obtained at almost all stages with an arbitrarily high probability, where efficiency is measured in terms of rate of convergence. It is further shown that such an optimal policy does not exist in the imperfect monitoring case. Moreover, it is proved that in the perfect monitoring case there does not exist a deterministic policy that satisfies our long run optimality criterion. In addition, we discuss the maxmin criterion and prove that a deterministic efficient optimal strategy does exist in the imperfect monitoring case under this criterion. Finally we show that our approach to long-run optimality can be viewed as qualitative, which distinguishes it from previous work in this area.Comment: See http://www.jair.org/ for any accompanying file

Fast Approximate Max-n Monte Carlo Tree Search for Ms Pac-Man

We present an application of Monte Carlo tree search (MCTS) for the game of Ms Pac-Man. Contrary to most applications of MCTS to date, Ms Pac-Man requires almost real-time decision making and does not have a natural end state. We approached the problem by performing Monte Carlo tree searches on a five player maxn tree representation of the game with limited tree search depth. We performed a number of experiments using both the MCTS game agents (for pacman and ghosts) and agents used in previous work (for ghosts). Performance-wise, our approach gets excellent scores, outperforming previous non-MCTS opponent approaches to the game by up to two orders of magnitude. © 2011 IEEE

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work