AlphaZero

AlphaZero is a computer program developed by artificial intelligence research company DeepMind to master the games of chess, shogi and go. This algorithm uses an approach similar to AlphaGo Zero.

On December 5, 2017, the DeepMind team released a preprint paper introducing AlphaZero, which would soon play three games by defeating world-champion chess engines Stockfish, Elmo, and the three-day version of AlphaGo Zero. In each case it made use of custom tensor processing units (TPUs) that the Google programs were optimized to use. AlphaZero was trained solely via self-play using 5,000 first-generation TPUs to generate the games and 64 second-generation TPUs to train the neural networks, all in parallel, with no access to opening books or endgame tables. After four hours of training, DeepMind estimated AlphaZero was playing chess at a higher Elo rating than Stockfish 8; after nine hours of training, the algorithm defeated Stockfish 8 in a time-controlled 100-game tournament (28 wins, 0 losses, and 72 draws). The trained algorithm played on a single machine with four TPUs.

DeepMind's paper on AlphaZero was published in the journal ''Science'' on 7 December 2018. While the actual AlphaZero program has not been released to the public, the algorithm described in the paper has been implemented in publicly available software. In 2019, DeepMind published a new paper detailing MuZero, a new algorithm able to generalize AlphaZero's work, playing both Atari and board games without knowledge of the rules or representations of the game.

Relation to AlphaGo Zero

AlphaZero (AZ) is a more generalized variant of the AlphaGo Zero (AGZ) algorithm, and is able to play shogi and chess as well as Go. Differences between AZ and AGZ include:

* AZ has hard-coded rules for setting search hyperparameters.
* The neural network is now updated continually.
* AZ doesn't use symmetries, unlike AGZ.
* Chess or Shogi can end in a draw unlike Go; therefore, AlphaZero takes into account the possibility of a drawn game.

Stockfish and Elmo

Comparing Monte Carlo tree search 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.

Training

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 neural networks. Training took several days, totaling about 41 TPU-years. It cost 3e22 FLOPs.

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.

Preliminary results

Outcome

Chess

In AlphaZero's chess match against Stockfish 8 (2016 TCEC world champion), each program was given one minute per move. AlphaZero was flying the English flag, while Stockfish the Norwegian. Stockfish was allocated 64 threads and a hash size of 1 GB, a setting that Stockfish's Tord Romstad later criticized as suboptimal. 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 TPUs. In 100 games from the normal starting position, AlphaZero won 25 games as White, won 3 as Black, and drew the remaining 72. 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.

Shogi

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. 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.

Go

After 34 hours of self-learning of Go and against AlphaGo Zero, AlphaZero won 60 games and lost 40.

Analysis

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 reinforcement learning 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." DeepMind's Demis Hassabis, 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."

Given the difficulty in chess of forcing a win against a strong opponent, the +28 –0 =72 result is a significant margin of victory. However, some grandmasters, such as Hikaru Nakamura