TDS+: Improving Temperature Discovery Search

Temperature Discovery Search (TDS) is a forward search method for computing or approximating the temperature of a combinatorial game. Temperature and mean are important concepts in combinatorial game theory, which can be used to develop efficient algorithms for playing well in a sum of subgames. A new algorithm TDS+ with five enhancements of TDS is developed, which greatly speeds up both exact and approximate versions of TDS. Means and temperatures can be computed faster, and fixed-time approximations which are important for practical play can be computed with higher accuracy than before.

[1]  Akihiro Kishimoto,et al.  A General Solution to the Graph History Interaction Problem , 2004, AAAI.

[2]  Richard J. Nowakowski,et al.  Lessons in Play: An Introduction to Combinatorial Game Theory , 2007 .

[3]  R Bellman.  ON THE APPLICATION OF DYNAMIC PROGRAMING TO THE DETERMINATION OF OPTIMAL PLAY IN CHESS AND CHECKERS. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Jonathan Schaeffer,et al.  Checkers Is Solved , 2007, Science.

[5]  Jonathan Schaeffer,et al.  CHINOOK: The World Man-Machine Checkers Champion , 1996, AI Mag..

[6]  Elwyn R. Berlekamp,et al.  Mathematical Go - chilling gets the last point , 1994 .

[7]  Jonathan Schaeffer,et al.  Kasparov versus Deep Blue: The Rematch , 1997, J. Int. Comput. Games Assoc..

[8]  Jonathan Schaeffer,et al.  Temperature Discovery Search , 2004, AAAI.

[9]  E. Berlekamp.  The Economist's View of Combinatorial Games , 1996 .

[10]  Martin Müller.  Decomposition Search: A Combinatorial Games Approach to Game Tree Search, with Applications to Solving Go Endgames , 1999, IJCAI.

[11]  Hiroyuki Iida,et al.  Playing Amazons Endgames , 2009, J. Int. Comput. Games Assoc..

[12]  L. Yedwab.  ON PLAYING WELL IN A SUM OF GAMES , 1985 .

[13]  Gerald Tesauro,et al.  Temporal difference learning and TD-Gammon , 1995, CACM.

[14]  Kuo-Yuan Kao.  Mean and Temperature Search for Go Endgames , 2000, Inf. Sci..

[15]  I-Chen Wu,et al.  Selection Search for Mean and Temperature of Multi-Branch Combinatorial Games , 2012, J. Int. Comput. Games Assoc..

[16]  Theodore. Tegos.  Shooting the last arrow , 2002 .

[17]  David Silver,et al.  Monte-Carlo tree search and rapid action value estimation in computer Go , 2011, Artif. Intell..

[18]  Simon M. Lucas,et al.  A Survey of Monte Carlo Tree Search Methods , 2012, IEEE Transactions on Computational Intelligence and AI in Games.

[19]  O. Hanner.  Mean play of sums of positional games , 1959 .

[20]  Elwyn R. Berlekamp.  Sums of n 2 amazons , 2000 .

[21]  Martin Müller,et al.  Fuego—An Open-Source Framework for Board Games and Go Engine Based on Monte Carlo Tree Search , 2010, IEEE Transactions on Computational Intelligence and AI in Games.

[22]  Akihiro Kishimoto,et al.  Game-Tree Search Using Proof Numbers: The First Twenty Years , 2012, J. Int. Comput. Games Assoc..

[23]  Takeaki Uno,et al.  Generalized Amazons is PSPACE-Complete , 2005, IJCAI.

[24]  Jiaxing Song,et al.  An Enhanced Solver for the Game of Amazons , 2015, IEEE Transactions on Computational Intelligence and AI in Games.

[25]  Jan. 9–Jan,et al.  Combinatorial Game Theory , 2022 .

[26]  Daisuke Takahashi,et al.  A Shogi Program Based on Monte-Carlo Tree Search , 2010, J. Int. Comput. Games Assoc..

[27]  A. Waters.  Winning ways. , 2002, Nursing standard (Royal College of Nursing (Great Britain) : 1987).

[28]  Ryan B. Hayward,et al.  Monte Carlo Tree Search in Hex , 2010, IEEE Transactions on Computational Intelligence and AI in Games.

[29]  Theodore Tegos,et al.  Experiments in Computer Amazons , 2002 .

[30]  Donald E. Knuth,et al.  The Solution for the Branching Factor of the Alpha-Beta Pruning Algorithm , 1981, ICALP.

[31]  Richard J. Lorentz.  Amazons Discover Monte-Carlo , 2008, Computers and Games.

[32]  Aaron N. Siegel.  Combinatorial Game Theory , 2013 .

[33]  Zhichao Li,et al.  Locally Informed Global Search for Sums of Combinatorial Games , 2004, Computers and Games.

[34]  J. Conway.  On Numbers and Games , 1976 .