Difference between revisions of "UCT"

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* [[Christopher D. Rosin]] ('''2011'''). ''[https://link.springer.com/article/10.1007/s10472-011-9258-6 Multi-armed bandits with episode context]''. Annals of Mathematics and Artificial Intelligence, Vol. 61, No. 3, [http://gauss.ececs.uc.edu/Workshops/isaim2010/papers/rosin.pdf ISAIM 2010 pdf] » [[Christopher D. Rosin#PUCT|PUCT]]
 
* [[Christopher D. Rosin]] ('''2011'''). ''[https://link.springer.com/article/10.1007/s10472-011-9258-6 Multi-armed bandits with episode context]''. Annals of Mathematics and Artificial Intelligence, Vol. 61, No. 3, [http://gauss.ececs.uc.edu/Workshops/isaim2010/papers/rosin.pdf ISAIM 2010 pdf] » [[Christopher D. Rosin#PUCT|PUCT]]
 
* [[Adrien Couëtoux]], [[Jean-Baptiste Hoock]], [[Nataliya Sokolovska]], [[Olivier Teytaud]], [[Nicolas Bonnard]] ('''2011'''). ''Continuous Upper Confidence Trees''. [https://dblp.uni-trier.de/db/conf/lion/lion2011.html LION 2011], [https://hal.archives-ouvertes.fr/hal-00542673v1/document pdf]
 
* [[Adrien Couëtoux]], [[Jean-Baptiste Hoock]], [[Nataliya Sokolovska]], [[Olivier Teytaud]], [[Nicolas Bonnard]] ('''2011'''). ''Continuous Upper Confidence Trees''. [https://dblp.uni-trier.de/db/conf/lion/lion2011.html LION 2011], [https://hal.archives-ouvertes.fr/hal-00542673v1/document pdf]
 +
* [[David Tolpin]], [[Solomon Eyal Shimony]] ('''2011'''). ''Doing Better Than UCT: Rational Monte Carlo Sampling in Trees''. [https://arxiv.org/abs/1108.3711 arXiv:1108.3711]
 
'''2012'''
 
'''2012'''
 
* [[Oleg Arenz]] ('''2012'''). ''Monte Carlo Chess''.  B.Sc. thesis, [[Darmstadt University of Technology]], advisor [[Johannes Fürnkranz]], [http://www.ke.tu-darmstadt.de/lehre/arbeiten/bachelor/2012/Arenz_Oleg.pdf pdf] » [[Stockfish]]
 
* [[Oleg Arenz]] ('''2012'''). ''Monte Carlo Chess''.  B.Sc. thesis, [[Darmstadt University of Technology]], advisor [[Johannes Fürnkranz]], [http://www.ke.tu-darmstadt.de/lehre/arbeiten/bachelor/2012/Arenz_Oleg.pdf pdf] » [[Stockfish]]
* [[Cameron Browne]], [[Simon Lucas]], et al. ('''2012'''). ''[http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6145622&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F4804728%2F6169178%2F06145622.pdf%3Farnumber%3D6145622 A Survey of Monte Carlo Tree Search Methods]''. [[IEEE#TOCIAIGAMES|IEEE Transactions on Computational Intelligence and AI in Games]], Vol. 4, [http://www.cameronius.com/cv/mcts-survey-master.pdf pdf]
+
* [[Cameron Browne]], [[Edward Powley]], [[Daniel Whitehouse]], [[Simon Lucas]], [[Peter Cowling]], [[Philipp Rohlfshagen]], [[Stephen Tavener]], [[Diego Perez]], [[Spyridon Samothrakis]], [[Simon Colton]] ('''2012'''). ''[https://ieeexplore.ieee.org/document/6145622 A Survey of Monte Carlo Tree Search Methods]''. [[IEEE#TOCIAIGAMES|IEEE Transactions on Computational Intelligence and AI in Games]], Vol. 4, No. 1, [http://ccg.doc.gold.ac.uk/ccg_old/papers/browne_tciaig12_1.pdf pdf]
 
* [[Sylvain Gelly]], [[Marc Schoenauer]], [[Michèle Sebag]], [[Olivier Teytaud]], [[Levente Kocsis]], [[David Silver]], [[Csaba Szepesvári]] ('''2012'''). ''[http://dl.acm.org/citation.cfm?id=2093548.2093574 The Grand Challenge of Computer Go: Monte Carlo Tree Search and Extensions]''. [[ACM#Communications|Communications of the ACM]], Vol. 55, No. 3, [http://www0.cs.ucl.ac.uk/staff/D.Silver/web/Applications_files/grand-challenge.pdf pdf preprint]
 
* [[Sylvain Gelly]], [[Marc Schoenauer]], [[Michèle Sebag]], [[Olivier Teytaud]], [[Levente Kocsis]], [[David Silver]], [[Csaba Szepesvári]] ('''2012'''). ''[http://dl.acm.org/citation.cfm?id=2093548.2093574 The Grand Challenge of Computer Go: Monte Carlo Tree Search and Extensions]''. [[ACM#Communications|Communications of the ACM]], Vol. 55, No. 3, [http://www0.cs.ucl.ac.uk/staff/D.Silver/web/Applications_files/grand-challenge.pdf pdf preprint]
 
* [[Adrien Couetoux]], [[Olivier Teytaud]], [[Hassen Doghmen]] ('''2012'''). ''Learning a Move-Generator for Upper Confidence Trees''. [http://ics2012.ndhu.edu.tw/ ICS 2012], [https://en.wikipedia.org/wiki/Hualien_City Hualien], [https://en.wikipedia.org/wiki/Taiwan Taiwan], December 2012 » [[Learning]], [[Move Generation]]
 
* [[Adrien Couetoux]], [[Olivier Teytaud]], [[Hassen Doghmen]] ('''2012'''). ''Learning a Move-Generator for Upper Confidence Trees''. [http://ics2012.ndhu.edu.tw/ ICS 2012], [https://en.wikipedia.org/wiki/Hualien_City Hualien], [https://en.wikipedia.org/wiki/Taiwan Taiwan], December 2012 » [[Learning]], [[Move Generation]]
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* [[Raghuram Ramanujan]], [[Ashish Sabharwal]], [[Bart Selman]] ('''2012'''). ''Understanding Sampling Style Adversarial Search Methods''. [http://arxiv.org/abs/1203.4011 arXiv:1203.4011]
 
* [[Raghuram Ramanujan]], [[Ashish Sabharwal]], [[Bart Selman]] ('''2012'''). ''Understanding Sampling Style Adversarial Search Methods''. [http://arxiv.org/abs/1203.4011 arXiv:1203.4011]
 
* [[Cheng-Wei Chou]], [[Ping-Chiang Chou]], [[Chang-Shing Lee]], [[David L. Saint-Pierre]], [[Olivier Teytaud]], [[Mei-Hui Wang]], [[Li-Wen Wu]], [[Shi-Jim Yen]] ('''2012'''). ''Strategic Choices: Small Budgets and Simple Regret''. [[TAAI 2012]], [http://www.csie.ndhu.edu.tw/csieweb/en/node/685 Excellent Paper Award], [https://hal.inria.fr/hal-00753145v2/document pdf]
 
* [[Cheng-Wei Chou]], [[Ping-Chiang Chou]], [[Chang-Shing Lee]], [[David L. Saint-Pierre]], [[Olivier Teytaud]], [[Mei-Hui Wang]], [[Li-Wen Wu]], [[Shi-Jim Yen]] ('''2012'''). ''Strategic Choices: Small Budgets and Simple Regret''. [[TAAI 2012]], [http://www.csie.ndhu.edu.tw/csieweb/en/node/685 Excellent Paper Award], [https://hal.inria.fr/hal-00753145v2/document pdf]
 +
* [[Arthur Guez]], [[David Silver]], [[Peter Dayan]] ('''2012'''). ''Efficient Bayes-Adaptive Reinforcement Learning using Sample-Based Search''. [https://arxiv.org/abs/1205.3109 arXiv:1205.3109]
 +
* [[Truong-Huy Dinh Nguyen]], [[Wee Sun Lee]], [[Tze-Yun Leong]] ('''2012'''). ''Bootstrapping Monte Carlo Tree Search with an Imperfect Heuristic''. [https://arxiv.org/abs/1206.5940 arXiv:1206.5940]
 +
* [[David Tolpin]], [[Solomon Eyal Shimony]] ('''2012'''). ''MCTS Based on Simple Regret''. [[Conferences#AAAI-2012|AAAI-2012]], [https://arxiv.org/abs/1207.5536 arXiv:1207.5536]
 
'''2013'''
 
'''2013'''
 
* [[Simon Viennot]], [[Kokolo Ikeda]] ('''2013'''). ''[http://link.springer.com/chapter/10.1007%2F978-3-319-09165-5_3 Efficiency of Static Knowledge Bias in Monte-Carlo Tree Search]''. [[CG 2013]]
 
* [[Simon Viennot]], [[Kokolo Ikeda]] ('''2013'''). ''[http://link.springer.com/chapter/10.1007%2F978-3-319-09165-5_3 Efficiency of Static Knowledge Bias in Monte-Carlo Tree Search]''. [[CG 2013]]
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* [[David W. King]] ('''2014'''). ''Complexity, Heuristic, and Search Analysis for the Games of Crossings and Epaminondas''. Masters thesis, [https://en.wikipedia.org/wiki/Air_Force_Institute_of_Technology Air Force Institute of Technology], [http://www.afit.edu/docs/AFIT-ENG-14-M-44_King.pdf pdf] <ref>[https://en.wikipedia.org/wiki/Crossings_%28game%29 Crossings from Wikipedia]</ref>
 
* [[David W. King]] ('''2014'''). ''Complexity, Heuristic, and Search Analysis for the Games of Crossings and Epaminondas''. Masters thesis, [https://en.wikipedia.org/wiki/Air_Force_Institute_of_Technology Air Force Institute of Technology], [http://www.afit.edu/docs/AFIT-ENG-14-M-44_King.pdf pdf] <ref>[https://en.wikipedia.org/wiki/Crossings_%28game%29 Crossings from Wikipedia]</ref>
 
* [[David W. King]], [[Gilbert L. Peterson]] ('''2014'''). ''Epaminondas: Exploring Combat Tactics''. [[ICGA Journal#37_3|ICGA Journal, Vol. 37, No. 3]] <ref> [https://en.wikipedia.org/wiki/Epaminondas_%28game%29 Epaminondas from Wikipedia]</ref>
 
* [[David W. King]], [[Gilbert L. Peterson]] ('''2014'''). ''Epaminondas: Exploring Combat Tactics''. [[ICGA Journal#37_3|ICGA Journal, Vol. 37, No. 3]] <ref> [https://en.wikipedia.org/wiki/Epaminondas_%28game%29 Epaminondas from Wikipedia]</ref>
* [[Truong-Huy Dinh Nguyen]], [[Wee Sun Lee]], [[Tze-Yun Leong]] ('''2012'''). ''Bootstrapping Monte Carlo Tree Search with an Imperfect Heuristic''. [https://arxiv.org/abs/1206.5940 arXiv:1206.5940]
 
 
* [[Truong-Huy Dinh Nguyen]], [[Tomi Silander]], [[Wee Sun Lee]], [[Tze-Yun Leong]] ('''2014'''). ''[https://www.aaai.org/ocs/index.php/ICAPS/ICAPS14/paper/view/7934 Bootstrapping Simulation-Based Algorithms with a Suboptimal Policy]''. [https://dblp.uni-trier.de/db/conf/aips/icaps2014.html ICAPS 2014], [https://youtu.be/ccwcZZj5vKM YouTube Video]
 
* [[Truong-Huy Dinh Nguyen]], [[Tomi Silander]], [[Wee Sun Lee]], [[Tze-Yun Leong]] ('''2014'''). ''[https://www.aaai.org/ocs/index.php/ICAPS/ICAPS14/paper/view/7934 Bootstrapping Simulation-Based Algorithms with a Suboptimal Policy]''. [https://dblp.uni-trier.de/db/conf/aips/icaps2014.html ICAPS 2014], [https://youtu.be/ccwcZZj5vKM YouTube Video]
 
==2015 ...==
 
==2015 ...==
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=Forum Posts=
 
=Forum Posts=
 +
==2010 ...==
 
* [http://computer-go.org/pipermail/computer-go/2010-June/000376.html Re: Chess vs Go // AI vs IA] by [[Gian-Carlo Pascutto]], June 02, 2010
 
* [http://computer-go.org/pipermail/computer-go/2010-June/000376.html Re: Chess vs Go // AI vs IA] by [[Gian-Carlo Pascutto]], June 02, 2010
 
* [http://www.lifein19x19.com/forum/viewtopic.php?f=18&t=2184 Monte Carlo (upper confidence bounds applied to trees)] by ChessGO, [http://www.lifein19x19.com/forum/viewforum.php?f=18 Computer Go], October 22, 2010
 
* [http://www.lifein19x19.com/forum/viewtopic.php?f=18&t=2184 Monte Carlo (upper confidence bounds applied to trees)] by ChessGO, [http://www.lifein19x19.com/forum/viewforum.php?f=18 Computer Go], October 22, 2010
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* [http://www.talkchess.com/forum/viewtopic.php?t=42590 uct on gpu] by [[Daniel Shawul]], [[CCC]], February 24, 2012 » [[GPU]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=42590 uct on gpu] by [[Daniel Shawul]], [[CCC]], February 24, 2012 » [[GPU]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=50721 My new book] by [[Daniel Shawul]], [[CCC]], January 02, 2014 » [[Opening Book]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=50721 My new book] by [[Daniel Shawul]], [[CCC]], January 02, 2014 » [[Opening Book]]
 +
==2015 ...==
 
* [http://www.talkchess.com/forum/viewtopic.php?t=65964 Nebiyu-MCTS vs TSCP 1-0] by [[Daniel Shawul]], [[CCC]], December 10, 2017 » [[Nebiyu]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=65964 Nebiyu-MCTS vs TSCP 1-0] by [[Daniel Shawul]], [[CCC]], December 10, 2017 » [[Nebiyu]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=66125 Search traps in MCTS and chess] by [[Daniel Shawul]], [[CCC]], December 25, 2017 » [[Raghuram Ramanujan#UCT|Sampling-Based Planning]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=66125 Search traps in MCTS and chess] by [[Daniel Shawul]], [[CCC]], December 25, 2017 » [[Raghuram Ramanujan#UCT|Sampling-Based Planning]]
 
* [http://rybkaforum.net/cgi-bin/rybkaforum/topic_show.pl?tid=32429 MCTS weakness wrt AB (via Daniel Shawul)] by [[Chris Whittington]], [[Computer Chess Forums|Rybka Forum]], December 25, 2017
 
* [http://rybkaforum.net/cgi-bin/rybkaforum/topic_show.pl?tid=32429 MCTS weakness wrt AB (via Daniel Shawul)] by [[Chris Whittington]], [[Computer Chess Forums|Rybka Forum]], December 25, 2017
 
* [http://www.talkchess.com/forum/viewtopic.php?t=66280 Announcing lczero] by [[Gary Linscott|Gary]], [[CCC]], January 09, 2018 » [[Leela Chess Zero]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=66280 Announcing lczero] by [[Gary Linscott|Gary]], [[CCC]], January 09, 2018 » [[Leela Chess Zero]]
 +
==2020 ...==
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=75484 uct algorithm bad at chess?] by Ofek Shochat, [[CCC]], October 21, 2020
  
 
=External Links=
 
=External Links=
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* [https://en.wikipedia.org/wiki/Confidence_interval Confidence interval from Wikipedia]
 
* [https://en.wikipedia.org/wiki/Confidence_interval Confidence interval from Wikipedia]
 
* [https://en.wikipedia.org/wiki/Multi-armed_bandit Multi-armed bandit from Wikipedia]
 
* [https://en.wikipedia.org/wiki/Multi-armed_bandit Multi-armed bandit from Wikipedia]
* [http://mcts.ai/about/index.html Monte Carlo Tree Search] by [[Cameron Browne]] et al.
+
* [https://github.com/theKGS/MCTS GitHub - theKGS/MCTS: Java implementation of UCT based MCTS and Flat MCTS]
: [http://mcts.ai/code/python.html UCT Monte Carlo Tree Search algorithm] in [[Python|Python 2.7]] by [[Peter Cowling]], [[Ed Powley]], and [[Daniel Whitehouse]]
+
* [https://senseis.xmp.net/?UCT Sensei's Library: UCT]
: [http://mcts.ai/code/java.html UCT MCTS implementation] in [[Java]] by [[Simon Lucas]]
+
* [https://althofer.de/lange-nacht-jena.html Lange Nacht der Wissenschaften - Long Night of Sciences Jena - 2007] by [[Ingo Althöfer]], [[Jakob Erdmann#UCT|MC and UCT poster]] by [[Jakob Erdmann]]
* [http://senseis.xmp.net/?UCT Sensei's Library: UCT]
 
* [http://www.althofer.de/lange-nacht-jena.html Lange Nacht der Wissenschaften - Long Night of Sciences Jena - 2007] by [[Ingo Althöfer]], [[Jakob Erdmann#UCT|MC and UCT poster]] by [[Jakob Erdmann]]
 
 
* [[:Category:Weather Report|Weather Report]] - [https://en.wikipedia.org/wiki/Sweetnighter Boogie Woogie Waltz], 1974, [https://en.wikipedia.org/wiki/YouTube YouTube] Video
 
* [[:Category:Weather Report|Weather Report]] - [https://en.wikipedia.org/wiki/Sweetnighter Boogie Woogie Waltz], 1974, [https://en.wikipedia.org/wiki/YouTube YouTube] Video
 
: [[:Category:Joe Zawinul|Joe Zawinul]], [[:Category:Wayne Shorter|Wayne Shorter]], [[:Category:Alphonso Johnson|Alphonso Johnson]], [https://www.allmusic.com/artist/darryl-brown-mn0001213839 Darryl Brown], [[:Category:Dom Um Romão|Dom Um Romão]]
 
: [[:Category:Joe Zawinul|Joe Zawinul]], [[:Category:Wayne Shorter|Wayne Shorter]], [[:Category:Alphonso Johnson|Alphonso Johnson]], [https://www.allmusic.com/artist/darryl-brown-mn0001213839 Darryl Brown], [[:Category:Dom Um Romão|Dom Um Romão]]
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'''[[Monte-Carlo Tree Search|Up one level]]'''
 
'''[[Monte-Carlo Tree Search|Up one level]]'''
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[[Category:Quotes]]
 
[[Category:Weather Report]]
 
[[Category:Weather Report]]
 
[[Category:Alphonso Johnson]]
 
[[Category:Alphonso Johnson]]

Latest revision as of 11:36, 23 October 2020

Home * Search * Monte-Carlo Tree Search * UCT

UCT (Upper Confidence bounds applied to Trees),
a popular algorithm that deals with the flaw of Monte-Carlo Tree Search, when a program may favor a losing move with only one or a few forced refutations, but due to the vast majority of other moves provides a better random playout score than other, better moves. UCT was introduced by Levente Kocsis and Csaba Szepesvári in 2006 [1], which accelerated the Monte-Carlo revolution in computer Go [2] and games difficult to evaluate statically. If given infinite time and memory, UCT theoretically converges to Minimax.

Selection

In UCT, upper confidence bounds (UCB1) guide the selection of a node [3], treating selection as a multi-armed bandit problem, where the crucial tradeoff the gambler faces at each trial is between exploration and exploitation - exploitation of the slot machine that has the highest expected payoff and exploration to get more information about the expected payoffs of the other machines. Child node j is selected which maximizes the UCT Evaluation:

UCTFormula.jpg

where:

  • Xj is the win ratio of the child
  • n is the number of times the parent has been visited
  • nj is the number of times the child has been visited
  • C is a constant to adjust the amount of exploration and incorporates the sqrt(2) from the UCB1 formula

The first component of the UCB1 formula above corresponds to exploitation, as it is high for moves with high average win ratio. The second component corresponds to exploration, since it is high for moves with few simulations.

RAVE

Most contemporary implementations of MCTS are based on some variant of UCT [4]. Modifications have been proposed, with the aim of shortening the time to find good moves. They can be divided into improvements based on expert knowledge and into domain-independent improvements in the playouts, and in building the tree in modifying the exploitation part of the UCB1 formula, for instance in Rapid Action Value Estimation (RAVE) [5] considering transpositions.

PUCT

Chris Rosin's PUCT modifies the original UCB1 multi-armed bandit policy by approximately predicting good arms at the start of a sequence of multi-armed bandit trials ('Predictor' + UCB = PUCB) [6]. A variation of PUCT was used in the AlphaGo and AlphaZero projects [7] , and subsequently also in Leela Zero and Leela Chess Zero [8].


Quotes

Gian-Carlo Pascutto

Quote by Gian-Carlo Pascutto in 2010 [9]:

There is no significant difference between an alpha-beta search with heavy LMR  and a static evaluator (current state of the art in chess) and an UCT searcher with a small exploration constant that does playouts (state of the art in go).
The shape of the tree they search is very similar. The main breakthrough in Go the last few years was how to backup an uncertain Monte Carlo score. This was solved. For chess this same problem was solved around the time quiescent search was developed.
Both are producing strong programs and we've proven for both the methods that they scale in strength as hardware speed goes up.
So I would say that we've successfully adopted the simple, brute force methods for chess to Go and they already work without increases in computer speed. The increases will make them progressively stronger though, and with further software tweaks they will eventually surpass humans. 

Raghuram Ramanujan et al.

Quote by Raghuram Ramanujan, Ashish Sabharwal, and Bart Selman from their abstract On Adversarial Search Spaces and Sampling-Based Planning [10]:

UCT has been shown to outperform traditional minimax based approaches in several challenging domains such as Go and KriegSpiel, although minimax search still prevails in other domains such as Chess. This work provides insights into the properties of adversarial search spaces that play a key role in the success or failure of UCT and similar sampling-based approaches. We show that certain "early loss" or "shallow trap" configurations, while unlikely in Go, occur surprisingly often in games like Chess (even in grandmaster games). We provide evidence that UCT, unlike minimax search, is unable to identify such traps in Chess and spends a great deal of time exploring much deeper game play than needed. 

See also

Publications

2000 ...

2005 ...

2006

2007

2008

2009

2010 ...

2011

2012

2013

2014

2015 ...

Forum Posts

2010 ...

2015 ...

2020 ...

External Links

Joe Zawinul, Wayne Shorter, Alphonso Johnson, Darryl Brown, Dom Um Romão

References

  1. Levente Kocsis, Csaba Szepesvári (2006). Bandit based Monte-Carlo Planning ECML-06, LNCS/LNAI 4212, pdf
  2. Sylvain Gelly, Marc Schoenauer, Michèle Sebag, Olivier Teytaud, Levente Kocsis, David Silver, Csaba Szepesvári (2012). The Grand Challenge of Computer Go: Monte Carlo Tree Search and Extensions. Communications of the ACM, Vol. 55, No. 3, pdf preprint
  3. see UCB1 in Peter Auer, Nicolò Cesa-Bianchi, Paul Fischer (2002). Finite-time Analysis of the Multiarmed Bandit Problem. Machine Learning, Vol. 47, No. 2
  4. Exploration and exploitation - in Monte Carlo tree search from Wikipedia
  5. Sylvain Gelly, David Silver (2011). Monte-Carlo tree search and rapid action value estimation in computer Go. Artificial Intelligence, Vol. 175, No. 11, preprint as pdf
  6. Christopher D. Rosin (2011). Multi-armed bandits with episode context. Annals of Mathematics and Artificial Intelligence, Vol. 61, No. 3, ISAIM 2010 pdf
  7. David Silver, Aja Huang, Chris J. Maddison, Arthur Guez, Laurent Sifre, George van den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel, Demis Hassabis (2016). Mastering the game of Go with deep neural networks and tree search. Nature, Vol. 529
  8. FAQ · LeelaChessZero/lc0 Wiki · GitHub
  9. Re: Chess vs Go // AI vs IA by Gian-Carlo Pascutto, June 02, 2010
  10. Raghuram Ramanujan, Ashish Sabharwal, Bart Selman (2010). On Adversarial Search Spaces and Sampling-Based Planning. ICAPS 2010
  11. Search traps in MCTS and chess by Daniel Shawul, CCC, December 25, 2017
  12. Crossings from Wikipedia
  13. Epaminondas from Wikipedia

Up one level