Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
AlphaZero
open-in-new
<h2 id="relation-to-alphago-zero">Relation to AlphaGo Zero</h2> <p class="note">Further information: <a href="/facts/AlphaGo_Zero/oUm1jEdz">AlphaGo Zero</a></p> <p>AlphaZero (AZ) is a more generalized variant of the AlphaGo Zero (AGZ) <a href="/facts/Algorithm/fnl5NmRt">algorithm</a>, and is able to play <a href="/facts/Shogi/z12HJ3vB">shogi</a> and <a href="/facts/Chess/47ykvkHF">chess</a> as well as <a href="/facts/Go_(game)/1fKhemww">Go</a>. Differences between AZ and AGZ include:<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> </p> <ul><li>AZ has hard-coded rules for setting search <a href="/facts/Hyperparameter_(machine_learning)/jCxm3fTA">hyperparameters</a>.</li> <li>The neural network is now updated continually.</li> <li>AZ doesn't use symmetries, unlike AGZ.</li> <li>Chess or Shogi can end in a <a href="/facts/Draw_(chess)/Q5fysWBJ">draw</a> unlike Go; therefore, AlphaZero takes into account the possibility of a drawn game.</li></ul> <h2 id="stockfish-and-elmo">Stockfish and Elmo</h2> <p class="note">Further information: <a href="/facts/Stockfish_(chess)/l8r2V9jK">Stockfish (chess)</a> and <a href="/facts/Elmo_(shogi_engine)/sjmgEsHK">elmo (shogi engine)</a></p> <p>Comparing <a href="/facts/Monte_Carlo_tree_search/ampuj7dk">Monte Carlo tree search</a> searches, AlphaZero searches just 80,000 positions per second in chess and 40,000 in shogi, compared to 70 million for Stockfish and 35 million for Elmo. AlphaZero compensates for the lower number of evaluations by using its deep neural network to focus much more selectively on the most promising variation.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> </p> <h2 id="training">Training</h2> <p>AlphaZero was trained by simply playing against itself multiple times, using 5,000 first-generation TPUs to generate the games and 64 second-generation TPUs to train the <a href="/facts/Neural_network/DDhJTfMc">neural networks</a>. Training took several days, totaling about 41 TPU-years. It cost 3e22 FLOPs.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> </p><p>In parallel, the in-training AlphaZero was periodically matched against its benchmark (Stockfish, Elmo, or AlphaGo Zero) in brief one-second-per-move games to determine how well the training was progressing. DeepMind judged that AlphaZero's performance exceeded the benchmark after around four hours of training for Stockfish, two hours for Elmo, and eight hours for AlphaGo Zero.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> </p> <h2 id="preliminary-results">Preliminary results</h2> <h3>Outcome</h3> <h4>Chess</h4> <p>In AlphaZero's chess match against Stockfish 8 (2016 <a href="/facts/Top_Chess_Engine_Championship/hXKLe7Nd">TCEC</a> world champion), each program was given one minute per move. AlphaZero was flying the English flag, while Stockfish the Norwegian.<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> Stockfish was allocated 64 threads and a <a href="/facts/Hash_table/Ht4ptDPF">hash</a> size of 1 GB,<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> a setting that Stockfish's Tord Romstad later criticized as suboptimal.<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a><a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> AlphaZero was trained on chess for a total of nine hours before the match. During the match, AlphaZero ran on a single machine with four application-specific <a href="/facts/Tensor_processing_unit/aVlg0LFF">TPUs</a>. In 100 games from the normal starting position, AlphaZero won 25 games as White, won 3 as Black, and drew the remaining 72.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> In a series of twelve, 100-game matches (of unspecified time or resource constraints) against Stockfish starting from the 12 most popular human openings, AlphaZero won 290, drew 886 and lost 24.<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> </p> <h4>Shogi</h4> <p>AlphaZero was trained on shogi for a total of two hours before the tournament. In 100 shogi games against Elmo (World Computer Shogi Championship 27 summer 2017 tournament version with YaneuraOu 4.73 search), AlphaZero won 90 times, lost 8 times and drew twice.<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a> As in the chess games, each program got one minute per move, and Elmo was given 64 threads and a hash size of 1 GB.<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a> </p> <h4>Go</h4> <p>After 34 hours of self-learning of Go and against AlphaGo Zero, AlphaZero won 60 games and lost 40.<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a><a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a> </p> <h3>Analysis</h3> <p>DeepMind stated in its preprint, "The game of chess represented the pinnacle of AI research over several decades. State-of-the-art programs are based on powerful engines that search many millions of positions, leveraging handcrafted domain expertise and sophisticated domain adaptations. AlphaZero is a generic <a href="/facts/Reinforcement_learning/NrgPPS0Q">reinforcement learning</a> algorithm – originally devised for the game of go – that achieved superior results within a few hours, searching a thousand times fewer positions, given no domain knowledge except the rules."<a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a> DeepMind's <a href="/facts/Demis_Hassabis/Cua93qw0">Demis Hassabis</a>, a chess player himself, called AlphaZero's play style "alien": It sometimes wins by offering counterintuitive sacrifices, like offering up a queen and bishop to exploit a positional advantage. "It's like chess from another dimension."<a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a> </p><p>Given the difficulty in chess of <a href="/facts/First-move_advantage_in_chess/mKwI68o8">forcing a win against a strong opponent</a>, the +28 –0 =72 result is a significant margin of victory. However, some grandmasters, such as <a href="/facts/Hikaru_Nakamura/k6dAxlK2">Hikaru Nakamura</a> and <a href="/facts/Komodo_(chess)/ad3JaqTE">Komodo</a> developer <a href="/facts/Larry_Kaufman/JKQvY1bw">Larry Kaufman</a>, downplayed AlphaZero's victory, arguing that the match would have been closer if the programs had access to an <a href="/facts/Chess_opening/lhWnwAd6">opening</a> database (since Stockfish was optimized for that scenario).<a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a> Romstad additionally pointed out that Stockfish is not optimized for rigidly fixed-time moves and the version used was a year old.<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a><a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a> </p><p>Similarly, some shogi observers argued that the Elmo hash size was too low, that the resignation settings and the "EnteringKingRule" settings (cf. <a href="/facts/Shogi/z12HJ3vB">shogi § Entering King</a>) may have been inappropriate, and that Elmo is already obsolete compared with newer programs.<a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a><a class="footnote-ref" id="fnref:29" href="#fn:29"><sup>29</sup></a> </p> <h3>Reaction and criticism</h3> <p>Papers headlined that the chess training took only four hours: "It was managed in little more than the time between breakfast and lunch."<a class="footnote-ref" id="fnref:30" href="#fn:30"><sup>30</sup></a><a class="footnote-ref" id="fnref:31" href="#fn:31"><sup>31</sup></a> <i><a href="/facts/Wired_(magazine)/RQb6gcyf">Wired</a></i> described AlphaZero as "the first multi-skilled AI board-game champ".<a class="footnote-ref" id="fnref:32" href="#fn:32"><sup>32</sup></a> AI expert Joanna Bryson noted that Google's "knack for good publicity" was putting it in a strong position against challengers. "It's not only about hiring the best programmers. It's also very political, as it helps make Google as strong as possible when negotiating with governments and regulators looking at the AI sector."<a class="footnote-ref" id="fnref:33" href="#fn:33"><sup>33</sup></a> </p><p>Human chess grandmasters generally expressed excitement about AlphaZero. Danish grandmaster <a href="/facts/Peter_Heine_Nielsen/8IjQdwfq">Peter Heine Nielsen</a> likened AlphaZero's play to that of a superior alien species.<a class="footnote-ref" id="fnref:34" href="#fn:34"><sup>34</sup></a> Norwegian grandmaster <a href="/facts/Jon_Ludvig_Hammer/xDbom6A4">Jon Ludvig Hammer</a> characterized AlphaZero's play as "insane attacking chess" with profound positional understanding.<a class="footnote-ref" id="fnref:35" href="#fn:35"><sup>35</sup></a> Former <a href="/facts/World_chess_champion/XPdyx85g">champion</a> <a href="/facts/Garry_Kasparov/NNjULdHH">Garry Kasparov</a> said, "It's a remarkable achievement, even if we should have expected it after AlphaGo."<a class="footnote-ref" id="fnref:36" href="#fn:36"><sup>36</sup></a><a class="footnote-ref" id="fnref:37" href="#fn:37"><sup>37</sup></a> </p><p>Grandmaster <a href="/facts/Hikaru_Nakamura/k6dAxlK2">Hikaru Nakamura</a> was less impressed, stating: "I don't necessarily put a lot of credibility in the results simply because my understanding is that AlphaZero is basically using the Google supercomputer and Stockfish doesn't run on that hardware; Stockfish was basically running on what would be my laptop. If you wanna have a match that's comparable you have to have Stockfish running on a supercomputer as well."<a class="footnote-ref" id="fnref:38" href="#fn:38"><sup>38</sup></a> </p><p>Top US correspondence chess player Wolff Morrow was also unimpressed, claiming that AlphaZero would probably not make the semifinals of a fair competition such as <a href="/facts/TCEC/hXKLe7Nd">TCEC</a> where all engines play on equal hardware. Morrow further stated that although he might not be able to beat AlphaZero if AlphaZero played drawish openings such as the <a href="/facts/Petroff_Defence/BQ16Gj1f">Petroff Defence</a>, AlphaZero would not be able to beat him in a <a href="/facts/Correspondence_chess/8P2VEh45">correspondence chess</a> game either.<a class="footnote-ref" id="fnref:39" href="#fn:39"><sup>39</sup></a> </p><p>Motohiro Isozaki, the author of YaneuraOu, noted that although AlphaZero did comprehensively beat Elmo, the rating of AlphaZero in shogi stopped growing at a point which is at most 100–200 higher than Elmo. This gap is not that high, and Elmo and other shogi software should be able to catch up in 1–2 years.<a class="footnote-ref" id="fnref:40" href="#fn:40"><sup>40</sup></a> </p> <h2 id="final-results">Final results</h2> <p>DeepMind addressed many of the criticisms in their final version of the paper, published in December 2018 in <i><a href="/facts/Science_(journal)/uTyzjkwD">Science</a></i>.<a class="footnote-ref" id="fnref:41" href="#fn:41"><sup>41</sup></a> They further clarified that AlphaZero was not running on a supercomputer; it was trained using 5,000 <a href="/facts/Tensor_processing_units/aVlg0LFF">tensor processing units</a> (TPUs), but only ran on four TPUs and a 44-core CPU in its matches.<a class="footnote-ref" id="fnref:42" href="#fn:42"><sup>42</sup></a> </p> <h3>Chess</h3> <p>In the final results, Stockfish 9 dev ran under the same conditions as in the <a href="/facts/Top_Chess_Engine_Championship/hXKLe7Nd">TCEC</a> superfinal: 44 CPU cores, Syzygy <a href="/facts/Endgame_tablebase/PSeEbcYT">endgame tablebases</a>, and a 32 GB hash size. Instead of a fixed <a href="/facts/Time_control/STuRXaHJ">time control</a> of one move per minute, both engines were given 3 hours plus 15 seconds per move to finish the game. AlphaZero ran on a much more powerful machine with four TPUs in addition to 44 CPU cores. In a 1000-game match, AlphaZero won with a score of 155 wins, 6 losses, and 839 draws. DeepMind also played a series of games using the TCEC opening positions; AlphaZero also won convincingly. Stockfish needed 10-to-1 time odds to match AlphaZero.<a class="footnote-ref" id="fnref:43" href="#fn:43"><sup>43</sup></a> </p> <h3>Shogi</h3> <p>Similar to Stockfish, Elmo ran under the same conditions as in the 2017 CSA championship. The version of Elmo used was WCSC27 in combination with YaneuraOu 2017 Early KPPT 4.79 64AVX2 TOURNAMENT. Elmo operated on the same hardware as Stockfish: 44 CPU cores and a 32 GB hash size. AlphaZero won 98.2% of games when playing sente (i.e. having the first move) and 91.2% overall. </p> <h3>Reactions and criticisms</h3> <p>Human grandmasters were generally impressed with AlphaZero's games against Stockfish.<a class="footnote-ref" id="fnref:44" href="#fn:44"><sup>44</sup></a> Former world champion <a href="/facts/Garry_Kasparov/NNjULdHH">Garry Kasparov</a> said it was a pleasure to watch AlphaZero play, especially since its style was open and dynamic like his own.<a class="footnote-ref" id="fnref:45" href="#fn:45"><sup>45</sup></a><a class="footnote-ref" id="fnref:46" href="#fn:46"><sup>46</sup></a> </p><p>In the computer chess community, <a href="/facts/Komodo_(chess)/ad3JaqTE">Komodo</a> developer Mark Lefler called it a "pretty amazing achievement", but also pointed out that the data was old, since Stockfish had gained a lot of strength since January 2018 (when Stockfish 8 was released). Fellow developer Larry Kaufman said AlphaZero would probably lose a match against the latest version of Stockfish, Stockfish 10, under Top Chess Engine Championship (TCEC) conditions. Kaufman argued that the only advantage of neural network–based engines was that they used a GPU, so if there was no regard for power consumption (e.g. in an equal-hardware contest where both engines had access to the same CPU and GPU) then anything the GPU achieved was "free". Based on this, he stated that the strongest engine was likely to be a hybrid with neural networks and standard <a href="/facts/Alpha%25E2%2580%2593beta_search/TRI5u3GL">alpha–beta search</a>.<a class="footnote-ref" id="fnref:47" href="#fn:47"><sup>47</sup></a> </p><p>AlphaZero inspired the computer chess community to develop <a href="/facts/Leela_Chess_Zero/D2u51yAY">Leela Chess Zero</a>, using the same techniques as AlphaZero. Leela contested several championships against Stockfish, where it showed roughly similar strength to Stockfish, although Stockfish has since pulled away.<a class="footnote-ref" id="fnref:48" href="#fn:48"><sup>48</sup></a> </p><p>In 2019 DeepMind published <a href="/facts/MuZero/mDU6F5rp">MuZero</a>, a unified system that played excellent chess, shogi, and go, as well as games in the <a href="/facts/Atari_2600/wSTCRAvp">Atari</a> Learning Environment, without being pre-programmed with their rules.<a class="footnote-ref" id="fnref:49" href="#fn:49"><sup>49</sup></a><a class="footnote-ref" id="fnref:50" href="#fn:50"><sup>50</sup></a> </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/AlphaGo/wJ9P2bBf">AlphaGo</a></li> <li><a href="/facts/AlphaDev/wFu4QPuL">AlphaDev</a></li> <li><a href="/facts/AlphaFold/DwBhppKC">AlphaFold</a></li> <li><a href="/facts/AlphaGeometry/bKDaLbbY">AlphaGeometry</a></li> <li><a href="/facts/General_game_playing/LEG0CGNb">General game playing</a> <ul><li><a href="/facts/MuZero/mDU6F5rp">MuZero</a></li></ul></li> <li><a href="/facts/Leela_Chess_Zero/D2u51yAY">Leela Chess Zero</a></li> <li><a href="/facts/Pluribus_(poker_bot)/MJ9SzUTA">Pluribus (poker bot)</a></li></ul> <h2 id="notes">Notes</h2> <h2 id="external-links">External links</h2> <ul><li><a href="https://www.chessprogramming.org/AlphaZero">Chessprogramming wiki on AlphaZero</a></li> <li><a href="https://www.youtube.com/watch?v=akgalUq5vew&list=PL-qLOQ-OEls607FPLAsPZ6De4f1W3ZF-I">Chess.com Youtube playlist for AlphaZero vs. Stockfish</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>"Silver" (PDF). idi.ntnu.no. <a href="https://www.idi.ntnu.no/emner/it3105/materials/neural/silver-2017b.pdf" target="_blank">https://www.idi.ntnu.no/emner/it3105/materials/neural/silver-2017b.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 5, 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". arXiv:1712.01815 [cs.AI]. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 5, 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". arXiv:1712.01815 [cs.AI]. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Knapton, Sarah; Watson, Leon (December 6, 2017). "Entire human chess knowledge learned and surpassed by DeepMind's AlphaZero in four hours". Telegraph.co.uk. Retrieved December 6, 2017. <a href="https://www.telegraph.co.uk/science/2017/12/06/entire-human-chess-knowledge-learned-surpassed-deepminds-alphazero/" target="_blank">https://www.telegraph.co.uk/science/2017/12/06/entire-human-chess-knowledge-learned-surpassed-deepminds-alphazero/</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Vincent, James (December 6, 2017). "DeepMind's AI became a superhuman chess player in a few hours, just for fun". The Verge. Retrieved December 6, 2017. <a href="https://www.theverge.com/2017/12/6/16741106/deepmind-ai-chess-alphazero-shogi-go" target="_blank">https://www.theverge.com/2017/12/6/16741106/deepmind-ai-chess-alphazero-shogi-go</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 7, 2018). "A general reinforcement learning algorithm that masters chess, shogi, and go through self-play". Science. 362 (6419): 1140–1144. Bibcode:2018Sci...362.1140S. doi:10.1126/science.aar6404. PMID 30523106. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>"Chess Terms: AlphaZero". Chess.com. Retrieved July 30, 2022. <a href="https://chess.com/terms/alphazero-chess-engine" target="_blank">https://chess.com/terms/alphazero-chess-engine</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Schrittwieser, Julian; Antonoglou, Ioannis; Hubert, Thomas; Simonyan, Karen; Sifre, Laurent; Schmitt, Simon; Guez, Arthur; Lockhart, Edward; Hassabis, Demis; Graepel, Thore; Lillicrap, Timothy (2020). "Mastering Atari, Go, chess and shogi by planning with a learned model". Nature. 588 (7839): 604–609. arXiv:1911.08265. Bibcode:2020Natur.588..604S. doi:10.1038/s41586-020-03051-4. PMID 33361790. S2CID 208158225. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 5, 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". arXiv:1712.01815 [cs.AI]. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 5, 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". arXiv:1712.01815 [cs.AI]. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>"Data on Notable AI Models". Epoch AI. June 19, 2024. Retrieved November 29, 2024. <a href="https://epoch.ai/data/notable-ai-models?view=table" target="_blank">https://epoch.ai/data/notable-ai-models?view=table</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 5, 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". arXiv:1712.01815 [cs.AI]. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>"AlphaZero vs. Stockfish 2017". <a href="https://chess24.com/en/embed-custom-tournament/condensed/alphazero-vs-stockfish" target="_blank">https://chess24.com/en/embed-custom-tournament/condensed/alphazero-vs-stockfish</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 5, 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". arXiv:1712.01815 [cs.AI]. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>"AlphaZero: Reactions From Top GMs, Stockfish Author". chess.com. December 8, 2017. Retrieved December 9, 2017. <a href="https://www.chess.com/news/view/alphazero-reactions-from-top-gms-stockfish-author" target="_blank">https://www.chess.com/news/view/alphazero-reactions-from-top-gms-stockfish-author</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Stockfish developer Tord Romstad responded with The match results by themselves are not particularly meaningful because of the rather strange choice of time controls and Stockfish parameter settings: The games were played at a fixed time of 1 minute/move, which means that Stockfish has no use of its time management heuristics (lot of effort has been put into making Stockfish identify critical points in the game and decide when to spend some extra time on a move; at a fixed time per move, the strength will suffer significantly). The version of Stockfish used is one year old, was playing with far more search threads than has ever received any significant amount of testing, and had way too small hash tables for the number of threads. I believe the percentage of draws would have been much higher in a match with more normal conditions.[10] <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>"'Superhuman' Google AI claims chess crown". BBC News. December 6, 2017. Retrieved December 7, 2017. <a href="https://www.bbc.com/news/technology-42251535" target="_blank">https://www.bbc.com/news/technology-42251535</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 5, 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". arXiv:1712.01815 [cs.AI]. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>"'Superhuman' Google AI claims chess crown". BBC News. December 6, 2017. Retrieved December 7, 2017. <a href="https://www.bbc.com/news/technology-42251535" target="_blank">https://www.bbc.com/news/technology-42251535</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> <li id="fn:20"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 5, 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". arXiv:1712.01815 [cs.AI]. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li> <li id="fn:21"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 5, 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". arXiv:1712.01815 [cs.AI]. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></p></li> <li id="fn:22"><p>"'Superhuman' Google AI claims chess crown". BBC News. December 6, 2017. Retrieved December 7, 2017. <a href="https://www.bbc.com/news/technology-42251535" target="_blank">https://www.bbc.com/news/technology-42251535</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></p></li> <li id="fn:23"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 5, 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". arXiv:1712.01815 [cs.AI]. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></p></li> <li id="fn:24"><p>Knight, Will (December 8, 2017). "Alpha Zero's "Alien" Chess Shows the Power, and the Peculiarity, of AI". MIT Technology Review. Retrieved December 11, 2017. <a href="https://www.technologyreview.com/s/609736/alpha-zeros-alien-chess-shows-the-power-and-the-peculiarity-of-ai/" target="_blank">https://www.technologyreview.com/s/609736/alpha-zeros-alien-chess-shows-the-power-and-the-peculiarity-of-ai/</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></p></li> <li id="fn:25"><p>"Google's AlphaZero Destroys Stockfish In 100-Game Match". Chess.com. Retrieved December 7, 2017. <a href="https://www.chess.com/news/view/google-s-alphazero-destroys-stockfish-in-100-game-match" target="_blank">https://www.chess.com/news/view/google-s-alphazero-destroys-stockfish-in-100-game-match</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></p></li> <li id="fn:26"><p>"AlphaZero: Reactions From Top GMs, Stockfish Author". chess.com. December 8, 2017. Retrieved December 9, 2017. <a href="https://www.chess.com/news/view/alphazero-reactions-from-top-gms-stockfish-author" target="_blank">https://www.chess.com/news/view/alphazero-reactions-from-top-gms-stockfish-author</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></p></li> <li id="fn:27"><p>Katyanna Quach. "DeepMind's AlphaZero AI clobbered rival chess app on non-level playing...board". The Register (December 14, 2017). <a href="https://www.theregister.co.uk/2017/12/14/deepmind_alphazero_ai_unfair" target="_blank">https://www.theregister.co.uk/2017/12/14/deepmind_alphazero_ai_unfair</a> <a href="#fnref:27" class="footnote-back-ref">↩</a></p></li> <li id="fn:28"><p>"Some concerns on the matching conditions between AlphaZero and Shogi engine". コンピュータ将棋 レーティング. "uuunuuun" (a blogger who rates free shogi engines). Retrieved December 9, 2017. (via "瀧澤 誠@elmo (@mktakizawa) | Twitter". mktakizawa (elmo developer). December 9, 2017. Retrieved December 11, 2017.) <a href="http://www.uuunuuun.com/single-post/2017/12/07/Some-concerns-on-the-matching-conditions-between-AlphaZero-and-Shogi-engine" target="_blank">http://www.uuunuuun.com/single-post/2017/12/07/Some-concerns-on-the-matching-conditions-between-AlphaZero-and-Shogi-engine</a> <a href="#fnref:28" class="footnote-back-ref">↩</a></p></li> <li id="fn:29"><p>"DeepMind社がやねうら王に注目し始めたようです". The developer of YaneuraOu, a search component used by elmo. December 7, 2017. Retrieved December 9, 2017. <a href="http://yaneuraou.yaneu.com/2017/12/07/deepmind%E7%A4%BE%E3%81%8C%E3%82%84%E3%81%AD%E3%81%86%E3%82%89%E7%8E%8B%E3%81%AB%E6%B3%A8%E7%9B%AE%E3%81%97%E5%A7%8B%E3%82%81%E3%81%9F%E3%82%88%E3%81%86%E3%81%A7%E3%81%99/" target="_blank">http://yaneuraou.yaneu.com/2017/12/07/deepmind%E7%A4%BE%E3%81%8C%E3%82%84%E3%81%AD%E3%81%86%E3%82%89%E7%8E%8B%E3%81%AB%E6%B3%A8%E7%9B%AE%E3%81%97%E5%A7%8B%E3%82%81%E3%81%9F%E3%82%88%E3%81%86%E3%81%A7%E3%81%99/</a> <a href="#fnref:29" class="footnote-back-ref">↩</a></p></li> <li id="fn:30"><p>Knapton, Sarah; Watson, Leon (December 6, 2017). "Entire human chess knowledge learned and surpassed by DeepMind's AlphaZero in four hours". Telegraph.co.uk. Retrieved December 6, 2017. <a href="https://www.telegraph.co.uk/science/2017/12/06/entire-human-chess-knowledge-learned-surpassed-deepminds-alphazero/" target="_blank">https://www.telegraph.co.uk/science/2017/12/06/entire-human-chess-knowledge-learned-surpassed-deepminds-alphazero/</a> <a href="#fnref:30" class="footnote-back-ref">↩</a></p></li> <li id="fn:31"><p>Badshah, Nadeem (December 7, 2017). "Google's DeepMind robot becomes world-beating chess grandmaster in four hours". The Times of London. Retrieved December 7, 2017. <a href="https://www.thetimes.com/business-money/technology/article/google-s-deepmind-alphazero-becomes-world-beating-chess-grandmaster-in-four-hours-hcppp9vr2" target="_blank">https://www.thetimes.com/business-money/technology/article/google-s-deepmind-alphazero-becomes-world-beating-chess-grandmaster-in-four-hours-hcppp9vr2</a> <a href="#fnref:31" class="footnote-back-ref">↩</a></p></li> <li id="fn:32"><p>"Alphabet's Latest AI Show Pony Has More Than One Trick". WIRED. December 6, 2017. Retrieved December 7, 2017. <a href="https://www.wired.com/story/alphabets-latest-ai-show-pony-has-more-than-one-trick/" target="_blank">https://www.wired.com/story/alphabets-latest-ai-show-pony-has-more-than-one-trick/</a> <a href="#fnref:32" class="footnote-back-ref">↩</a></p></li> <li id="fn:33"><p>"'Superhuman' Google AI claims chess crown". BBC News. December 6, 2017. Retrieved December 7, 2017. <a href="https://www.bbc.com/news/technology-42251535" target="_blank">https://www.bbc.com/news/technology-42251535</a> <a href="#fnref:33" class="footnote-back-ref">↩</a></p></li> <li id="fn:34"><p>"'Superhuman' Google AI claims chess crown". BBC News. December 6, 2017. Retrieved December 7, 2017. <a href="https://www.bbc.com/news/technology-42251535" target="_blank">https://www.bbc.com/news/technology-42251535</a> <a href="#fnref:34" class="footnote-back-ref">↩</a></p></li> <li id="fn:35"><p>Knapton, Sarah; Watson, Leon (December 6, 2017). "Entire human chess knowledge learned and surpassed by DeepMind's AlphaZero in four hours". Telegraph.co.uk. Retrieved December 6, 2017. <a href="https://www.telegraph.co.uk/science/2017/12/06/entire-human-chess-knowledge-learned-surpassed-deepminds-alphazero/" target="_blank">https://www.telegraph.co.uk/science/2017/12/06/entire-human-chess-knowledge-learned-surpassed-deepminds-alphazero/</a> <a href="#fnref:35" class="footnote-back-ref">↩</a></p></li> <li id="fn:36"><p>"Google's AlphaZero Destroys Stockfish In 100-Game Match". Chess.com. Retrieved December 7, 2017. <a href="https://www.chess.com/news/view/google-s-alphazero-destroys-stockfish-in-100-game-match" target="_blank">https://www.chess.com/news/view/google-s-alphazero-destroys-stockfish-in-100-game-match</a> <a href="#fnref:36" class="footnote-back-ref">↩</a></p></li> <li id="fn:37"><p>Gibbs, Samuel (December 7, 2017). "AlphaZero AI beats champion chess program after teaching itself in four hours". The Guardian. Retrieved December 8, 2017. <a href="https://www.theguardian.com/technology/2017/dec/07/alphazero-google-deepmind-ai-beats-champion-program-teaching-itself-to-play-four-hours" target="_blank">https://www.theguardian.com/technology/2017/dec/07/alphazero-google-deepmind-ai-beats-champion-program-teaching-itself-to-play-four-hours</a> <a href="#fnref:37" class="footnote-back-ref">↩</a></p></li> <li id="fn:38"><p>"AlphaZero: Reactions From Top GMs, Stockfish Author". chess.com. December 8, 2017. Retrieved December 9, 2017. <a href="https://www.chess.com/news/view/alphazero-reactions-from-top-gms-stockfish-author" target="_blank">https://www.chess.com/news/view/alphazero-reactions-from-top-gms-stockfish-author</a> <a href="#fnref:38" class="footnote-back-ref">↩</a></p></li> <li id="fn:39"><p>"Talking modern correspondence chess". Chessbase. June 26, 2018. Retrieved July 11, 2018. <a href="https://en.chessbase.com/post/correspondence-chess-and-correspondence-database-2018" target="_blank">https://en.chessbase.com/post/correspondence-chess-and-correspondence-database-2018</a> <a href="#fnref:39" class="footnote-back-ref">↩</a></p></li> <li id="fn:40"><p>DeepMind社がやねうら王に注目し始めたようです | やねうら王 公式サイト, 2017年12月7日 <a href="http://yaneuraou.yaneu.com/2017/12/07/deepmind%E7%A4%BE%E3%81%8C%E3%82%84%E3%81%AD%E3%81%86%E3%82%89%E7%8E%8B%E3%81%AB%E6%B3%A8%E7%9B%AE%E3%81%97%E5%A7%8B%E3%82%81%E3%81%9F%E3%82%88%E3%81%86%E3%81%A7%E3%81%99/" target="_blank">http://yaneuraou.yaneu.com/2017/12/07/deepmind%E7%A4%BE%E3%81%8C%E3%82%84%E3%81%AD%E3%81%86%E3%82%89%E7%8E%8B%E3%81%AB%E6%B3%A8%E7%9B%AE%E3%81%97%E5%A7%8B%E3%82%81%E3%81%9F%E3%82%88%E3%81%86%E3%81%A7%E3%81%99/</a> <a href="#fnref:40" class="footnote-back-ref">↩</a></p></li> <li id="fn:41"><p>Silver, David; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; Kumaran, Dharshan; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; Hassabis, Demis (December 7, 2018). "A general reinforcement learning algorithm that masters chess, shogi, and go through self-play". Science. 362 (6419): 1140–1144. Bibcode:2018Sci...362.1140S. doi:10.1126/science.aar6404. PMID 30523106. <a href="/wiki/David_Silver_(computer_scientist)" target="_blank">/wiki/David_Silver_(computer_scientist)</a> <a href="#fnref:41" class="footnote-back-ref">↩</a></p></li> <li id="fn:42"><p>As given in the Science paper, a TPU is "roughly similar in inference speed to a Titan V GPU, although the architectures are not directly comparable" (Ref. 24). <a href="#fnref:42" class="footnote-back-ref">↩</a></p></li> <li id="fn:43"><p>"AlphaZero Crushes Stockfish In New 1,000-Game Match". December 6, 2018. <a href="https://www.chess.com/news/view/updated-alphazero-crushes-stockfish-in-new-1-000-game-match" target="_blank">https://www.chess.com/news/view/updated-alphazero-crushes-stockfish-in-new-1-000-game-match</a> <a href="#fnref:43" class="footnote-back-ref">↩</a></p></li> <li id="fn:44"><p>"AlphaZero Crushes Stockfish In New 1,000-Game Match". December 6, 2018. <a href="https://www.chess.com/news/view/updated-alphazero-crushes-stockfish-in-new-1-000-game-match" target="_blank">https://www.chess.com/news/view/updated-alphazero-crushes-stockfish-in-new-1-000-game-match</a> <a href="#fnref:44" class="footnote-back-ref">↩</a></p></li> <li id="fn:45"><p>Sean Ingle (December 11, 2018). "'Creative' AlphaZero leads way for chess computers and, maybe, science". The Guardian. <a href="https://www.theguardian.com/sport/2018/dec/11/creative-alphazero-leads-way-chess-computers-science" target="_blank">https://www.theguardian.com/sport/2018/dec/11/creative-alphazero-leads-way-chess-computers-science</a> <a href="#fnref:45" class="footnote-back-ref">↩</a></p></li> <li id="fn:46"><p>Albert Silver (December 7, 2018). "Inside the (deep) mind of AlphaZero". Chessbase. <a href="https://en.chessbase.com/post/the-full-alphazero-paper-is-published-at-long-last" target="_blank">https://en.chessbase.com/post/the-full-alphazero-paper-is-published-at-long-last</a> <a href="#fnref:46" class="footnote-back-ref">↩</a></p></li> <li id="fn:47"><p>"Komodo MCTS (Monte Carlo Tree Search) is the new star of TCEC". Chessdom. December 18, 2018. <a href="http://www.chessdom.com/komodo-mcts-monte-carlo-tree-search-is-the-new-star-of-tcec/" target="_blank">http://www.chessdom.com/komodo-mcts-monte-carlo-tree-search-is-the-new-star-of-tcec/</a> <a href="#fnref:47" class="footnote-back-ref">↩</a></p></li> <li id="fn:48"><p>See TCEC and Leela Chess Zero. <a href="/wiki/TCEC" target="_blank">/wiki/TCEC</a> <a href="#fnref:48" class="footnote-back-ref">↩</a></p></li> <li id="fn:49"><p>"Could Artificial Intelligence Save Us From Itself?". Fortune. 2019. Retrieved February 29, 2020. <a href="https://fortune.com/2019/11/26/ai-is-the-problem-and-the-solution/" target="_blank">https://fortune.com/2019/11/26/ai-is-the-problem-and-the-solution/</a> <a href="#fnref:49" class="footnote-back-ref">↩</a></p></li> <li id="fn:50"><p>"DeepMind's MuZero teaches itself how to win at Atari, chess, shogi, and Go". VentureBeat. November 20, 2019. Retrieved February 29, 2020. <a href="https://venturebeat.com/2019/11/20/deepminds-muzero-teaches-itself-how-to-win-at-atari-chess-shogi-and-go/" target="_blank">https://venturebeat.com/2019/11/20/deepminds-muzero-teaches-itself-how-to-win-at-atari-chess-shogi-and-go/</a> <a href="#fnref:50" class="footnote-back-ref">↩</a></p></li> </ol>