Keyword(s):Probability, Monte-Carlo Simulations, Proof Number Search, Game Solver.

Abstract: Probability based proof number search (PPN-search) is a game tree search algorithm improved from proof number search (PN-search) (Allis et al., 1994), with applications in solving games or endgame positions. PPN-search uses one indicator named “probability based proof number” (PPN) to indicate the “probability” of proving a node. The PPN of a leaf node is derived from Monte-Carlo evaluations. The PPN of an internal node is backpropagated from its children following AND/OR probability rules. For each iteration, PPN-search selects the child with the maximum PPN at OR nodes and minimum PPN at AND nodes. This holds from the root to a leaf. The resultant node is considered to be the most proving node for expansion. In this paper, we investigate the performance of PPN-search on P-game trees (Kocsis and Szepesvári, 2006) and compare our results with those from other game solvers such as MCPN-search (Saito et al., 2006), PN-search, the UCT solver (Winands et al., 2008), and the pure MCTS solver (Winands et al., 2008). The experimental results show that (1) PPN-search takes less time and fewer iterations to solve a P-game tree on average, and (2) the error rate of selecting a correct solution decreases faster and more smoothly as the iteration number increases.(More)

Probability based proof number search (PPN-search) is a game tree search algorithm improved from proof number search (PN-search) (Allis et al., 1994), with applications in solving games or endgame positions. PPN-search uses one indicator named “probability based proof number” (PPN) to indicate the “probability” of proving a node. The PPN of a leaf node is derived from Monte-Carlo evaluations. The PPN of an internal node is backpropagated from its children following AND/OR probability rules. For each iteration, PPN-search selects the child with the maximum PPN at OR nodes and minimum PPN at AND nodes. This holds from the root to a leaf. The resultant node is considered to be the most proving node for expansion. In this paper, we investigate the performance of PPN-search on P-game trees (Kocsis and Szepesvári, 2006) and compare our results with those from other game solvers such as MCPN-search (Saito et al., 2006), PN-search, the UCT solver (Winands et al., 2008), and the pure MCTS solver (Winands et al., 2008). The experimental results show that (1) PPN-search takes less time and fewer iterations to solve a P-game tree on average, and (2) the error rate of selecting a correct solution decreases faster and more smoothly as the iteration number increases.

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Song, Z.; Iida, H. and van den Herik, H. (2019). Probability based Proof Number Search.In Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-350-6, pages 661-668. DOI: 10.5220/0007386806610668

@conference{icaart19, author={Zhang Song. and Hiroyuki Iida. and H. Jaap van den Herik.}, title={Probability based Proof Number Search}, booktitle={Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,}, year={2019}, pages={661-668}, publisher={SciTePress}, organization={INSTICC}, doi={10.5220/0007386806610668}, isbn={978-989-758-350-6}, }

TY - CONF

JO - Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, TI - Probability based Proof Number Search SN - 978-989-758-350-6 AU - Song, Z. AU - Iida, H. AU - van den Herik, H. PY - 2019 SP - 661 EP - 668 DO - 10.5220/0007386806610668