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Real-time Solving of Quantified CSPs based on Monte-Carlo Game Tree Search

Satomi Baba, Yongjoon Joe, Atsushi Iwasaki and Makoto Yokoo

We develop a real-time algorithm based on a Monte-Carlo game tree search for solving a quantified constraint satisfaction problem (QCSP) . A QCSP is a CSP where some variables are universally quantified. A universally quantified variable represents a choice of the nature or an adversary. The goal of a QCSP is to make a robust plan against an adversary. However, obtaining a complete plan off-line is intractable when the size of the problem becomes large. Thus, we need to develop a real-time algorithm that selects a promising value sequentially at each deadline. Such a problem has been considered in the field of game tree search. In a standard game tree search algorithm, developing a good static evaluation function is crucial. However, developing a good static evaluation function for a QCSP is very difficult. Thus, we apply a Monte-Carlo game tree search technique called UCT. However, the simple application of the UCT algorithm does not work since the player and the adversary are asymmetric. We overcome this difficulty by introducing constraint propagation techniques. We experimentally compare the winning probability of our UCT-based algorithm and the state-of-the-art alpha-beta search algorithm and show that our algorithms outperforms the state-of-the-art algorithm in large-scale problems.