Probability based Proof Number Search

Zhang Song, Hiroyuki Iida, H. van den Herik

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.

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Paper Citation


in Harvard Style

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


in Bibtex Style

@conference{icaart19,
author={Zhang Song and Hiroyuki Iida and H. 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},
}


in EndNote Style

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