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AlphaZero,
a chess and Go playing entity by Google DeepMind based on a general reinforcement learning algorithm with the same name. On December 5, 2017, the DeepMind team around David Silver, Thomas Hubert, and Julian Schrittwieser along with former Giraffe author Matthew Lai, reported on their generalized algorithm, combining Deep learning with Monte-Carlo Tree Search (MCTS) [1] .

A 100 game match versus Stockfish 8 using 64 threads and a transposition table size of 1GiB, was won by AlphaZero using a single machine with 4 Tensor processing units (TPUs) with +28=72-0. Despite a possible hardware advantage of AlphaZero and criticized playing conditions [2], this seems a tremendous achievement.
The Krampus has come [3] [4]

Description

Starting from random play, and given no domain knowledge except the game rules, AlphaZero achieved a superhuman level of play in the games of chess and Shogi as well as in Go. The algorithm is a more generic version of the AlphaGo Zero algorithm that was first introduced in the domain of Go [5] . AlphaZero evaluates positions using non-linear function approximation based on a deep neural network, rather than the linear function approximation as used in classical chess programs. This neural network takes the board position as input and outputs a vector of move probabilities. The MCTS consists of a series of simulated games of self-play whose move selection is controlled by the neural network. The search returns a vector representing a probability distribution over moves, either proportionally or greedily with respect to the visit counts at the root state.

Network Architecture

The network is a deep residual convolutional neural network [6] [7] with many layers of spatial NxN planes - 8x8 board arrays for chess. The input describes the chess position from side's to move point of view - that is color flipped for black to move. Each square cell consists of 12 piece-type and color bits, e.g. from the current bitboard board definition, and to address graph history and path-dependency - times eight, that is up to seven predecessor positions as well - so that en passant, immediate repetitions, or some sense of progress is implicit. Additional inputs, redundant inside each square cell to be conform to the convolution net, consider castling rights, halfmove clock, total move count and side to move.

The deep hidden layers connect the pieces on different squares to each other due to consecutive 3x3 convolutions, where a cell of a layer is connected to the correspondent 3x3 receptive field of the previous layer, so that after 4 layers, each square is connected to every other cell in the original input layer [8]. The output of the neural network is finally represented as an 8x8 board array as well, for every origin square up to 73 target square possibilities (NRayDirs x MaxRayLength + NKnightDirs + NPawnDirs * NMinorPromotions), encoding a probability distribution over 64x73 = 4,672 possible moves, where illegal moves were masked out by setting their probabilities to zero, re-normalising the probabilities for remaining moves.

Training

AlphaZero was trained in 700,000 steps or mini-batches of size 4096 each, starting from randomly initialized parameters, using 5,000 first-generation TPUs [9] to generate self-play games and 64 second-generation TPUs [10] [11] [12] to train the neural networks [13] .

See also


Publications


Forum Posts

2017

2018


External Links

Reports

Stockfish Match

Misc


References

  1. ^ David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, Timothy Lillicrap, Karen Simonyan, Demis Hassabis (2017). Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm. arXiv:1712.01815
  2. ^ Alpha Zero by BB+, OpenChess Forum, December 06, 2017
  3. ^ Krampus at Perchtenlauf in Klagenfurt, Image by Anita Martinz, December 02, 2006, CC BY 2.0, Wikimedia Commons
  4. ^ "5th of December - The Krampus has come" was suggested by Michael Scheidl in AlphaZero by Peter Martan, CSS Forum, December 06, 2017, with further comments by Ingo Althöfer
  5. ^ AlphaGo Zero: Learning from scratch by Demis Hassabis and David Silver, DeepMind, October 18, 2017
  6. ^ The principle of residual nets is to add the input of the layer to the output of each layer. With this simple modification training is faster and enables deeper networks, see Tristan Cazenave (2017). Residual Networks for Computer Go. IEEE Transactions on Computational Intelligence and AI in Games, Vol. PP, No. 99, pdf
  7. ^ Residual Networks for Computer Go by Brahim Hamadicharef, CCC, December 07, 2017
  8. ^ Re: AlphaZero is not like other chess programs by Rein Halbersma, CCC, December 09, 2017
  9. ^ First In-Depth Look at Google’s TPU Architecture by Nicole Hemsoth, The Next Platform, April 05, 2017
  10. ^ Photo of Google Cloud TPU cluster by Norman Schmidt, CCC, December 09, 2017
  11. ^ First In-Depth Look at Google’s New Second-Generation TPU by Nicole Hemsoth, The Next Platform, May 17, 2017
  12. ^ Under The Hood Of Google’s TPU2 Machine Learning Clusters by Paul Teich, The Next Platform, May 22, 2017
  13. ^ David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, Timothy Lillicrap, Karen Simonyan, Demis Hassabis (2017). Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm. arXiv:1712.01815
  14. ^ AlphaZero explained by one creator by Mario Carbonell Martinez, CCC, December 19, 2017
  15. ^ A Simple Alpha(Go) Zero Tutorial by Oliver Roese, CCC, December 30, 2017
  16. ^ BBC News; 'Google's ... DeepMind AI claims chess crown' by pennine22, Hiarcs Forum, December 07, 2017
  17. ^ Reactions about AlphaZero from top GMs... by Norman Schmidt, CCC, December 08, 2017
  18. ^ recent article on alphazero ... 12/11/2017 ... by Dan Ellwein, CCC, December 14, 2017
  19. ^ Cerebellum analysis of the AlphaZero - Stockfish Games by Thomas Zipproth, CCC, December 11, 2017
  20. ^ AlphaZero reinvents mobility and romanticism by Chris Whittington, Rybka Forum, December 08, 2017
  21. ^ Immortal Zugzwang Game from Wikipedia
  22. ^ Article:"How Alpha Zero Sees/Wins" by AA Ross, CCC, January 17, 2018

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