49

No, it can't. Even if you had it train on a zillion self-playing games and it miraculously achieved perfect play somehow, we would have no way of proving that it had achieved perfect play without first solving chess some other way and then comparing AlphaZero's play to perfect play in all possible positions. Its approach simply doesn't result in a solution ...


48

Other answers are right in that AlphaZero was implicitly told that castling is a move that exists, I'll elaborate on how exactly that happens by explaining the inputs and outputs of the neural network. Input format At the core of AlphaZero is a neural network, which gets as an input the current board state. This board state is encoded as a stack of images, ...


46

was AlphaZero just given this move It was given this move in the same way that it was given all other moves. It started with complete knowledge of the rules of the game. In machine learning terms, castling would be part of its baseline knowledge of state transitions.


36

Page 5 in the paper has your answer: ... AlphaZero compensates for the lower number of evaluations by using its deep neural network to costs much more selectively on the most promising variations - arguably a more "human-like" approach to chess ... "selectively" is the key word. What does that mean? Let's use this following position for our example: ...


27

It sort of did. "Sort of" because once you examine how neural networks work it's not clear what AlphaZero is actually learning. AlphaZero has a neural network evaluation function. How that works is that it takes as input the position on the board (along with other things like whether a pawn can capture en passant, whether castling is possible, etc) ...


23

How does AlphaZero select a move in the search? This is very obvious from the paper. Each simulation proceeds by selecting in each state s a move a with low visit count, high move probability and high vale selecting ... What does that mean? AlphaZero has trained probabilities for each move (end of page 2 in the paper) from a deep neural network. During ...


22

That's why I wonder whether there have been any attempts made to provide comparable hardware to both. This is Google you're talking about! So the answer is obviously "No". From the original paper hardware used for initialising and training - Training proceeded for 700,000 steps (mini-batches of size 4,096) starting from randomly initialised ...


18

Most strong engines emphasize looking very deeply, at the expense of having a superficial evaluation function. In the AlphaZero paper, they say that Stockfish looks at 70 million positions per second. Human grandmasters look at very few positions indeed compared to engines, but they have a better feeling who is better in a given position. AlphaZero looked ...


15

The short answer is: No. AlphaZero learns to evaluate only the position. The position consists of all the pieces and their placement on the board (plus castling and en-passant information). There is no way to distinguish the material's value from the position's strength -- which is a really beautiful idea and offers a lot of learning potential for humans. ...


14

We can't say for sure since AlphaZero is a private engine, i.e. we don't have games between it and the latest versions of Stockfish. Still, if AlphaZero hasn't improved since it was unveiled, it will likely lose to the latest version of Stockfish. That's because AlphaZero beat Stockfish 8 by +155 = 839 -6, which is an elo difference of about 50. The latest ...


13

AlphaZero already seems to play like a regular "centaur" -> correspodence GM with an engine assistance. As an FM I'd get much more enjoyment of playing AlphaZero vs a regular engine. One comparison would be it plays like Karpov would with perfect tactics. (Game 9 AlphaZero plays a piece down for 15moves which is very Tal like). It is not just style, ...


13

I think it's best if I elaborate on your second point with an example move in the game 1 between AlphaZero and Stockfish which also served to satisfy my curiosity today. the time limit of 1 min/move (How would this disadvantage Stockfish?) Stockfish's performance is dependent upon both the time limit and the hardware configuration, so just think of when ...


12

AlphaZero hasn't solved chess, and it won't until it can find a strategy that results in the same outcome of the game given perfect play from both sides. According to Wikipedia: A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly. Since AlphaZero has lost games ...


12

Check out the AlphaZero paper, figure 1. As you can see from the leftmost figure, you can let AlphaZero train, but that doesn't mean it'll improve. In fact, AlphaZero peaked at a level slightly above Stockfish 8 (in other words, it'll likely lose to Stockfish 10). I'm no expert, but I understand Leela is competitive with Stockfish 10 not because she has ...


12

The AlphaZero paper "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm" by David Silver et al. contains this explanation Knowledge of the rules is also used to encode the input planes (i.e. castling, repetition, no-progress) and output planes (how pieces move, promotions, and piece drops in shogi). (An input ...


11

You can find the complete table in their paper. See table 2 in the arXiv version linked below: Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm https://arxiv.org/pdf/1712.01815.pdf How to read them: The plots show the proportion of times alphazero played a given opening during its self-training games as a function of ...


10

EDIT @unutbu's link in the comment is a good introductory read. Solid understanding for AlphaZero most likely require a quantitative degree (PhD?). Are you asking for a crash course in AlphaZero? Please note unless you invest significant amount of your time, nothing I say will work. There is no book that can possibly cover everything. You will need to ...


10

In short, because DeepMind has TPUs. Lots and lots of TPUs. By far, the most time-consuming part of the training process is generating self-play games. DeepMind used 5000 TPUs to generate self-play games, which is a lot of processing power. Meanwhile, Lc0 crowdsources processing power from volunteer clients, which is much slower. From the DeepMind paper ...


9

Both Nakamura and the StackExchange answer were correct - Stockfish didn't use an opening book. I think Google did that to make a fair comparison as AlphaZero wasn't using an opening book as well. EDIT I didn't see anything about opening book for Stockfish in the paper. I'm not the only one. http://talkchess.com/forum/viewtopic.php?t=65910&postdays=0&...


9

It is as easy to jump on a bandwagon saying Alpha-Zero's play is 'more' human than previous computer chess programs as it is to jump on the opposite wagon and say Alpha-Zero's play is entirely 'alien'. It's not clear that Alpha-zero's play is 'more human' especially given our human tendency towards anthropomorphism. Chess as a Struggle of the (human) Mind ...


9

TLDR: No Reasoning: Quantum Computers in the short to medium term only have some very specific things efficiently (factoring and discrete log and a few others). The algorithm google showed "quantum supremecy" on is basically simulating a random quantum circuit to generate random numbers, which is about as favorable an algorithm as you could imagine ...


8

The evaluation function of a chess engine, whether instantiated as a neural net or explicit code, is always able to assign a value to any board position. If you give it a board position, even absurd ones that would never occur in a game, it will be able to spit out a number representing how favorable it is to one player or another. Since the number of board ...


8

Here's an online calculator for this. 28 wins, 0 losses, and 72 draws is an elo difference of exactly 100. Do remember that this score +28 =72 -0 score was against a handicapped version of Stockfish. In the full paper, AlphaZero scored +155 =839 -6, which is an elo difference of 52.


8

Nope. AlphaZero's entire architecture (and the architectures of most other engines) is such that it cannot "find a solution", and in any case, if a solution was to be found it would be through programs meant to do just that. Such programs do not exist, due to the absurd complexity. Also, note that AlphaZero (as far as I know) is no longer under ...


8

One central piece of alphazero is the neural evaluation function. This function takes the board as input and produces a value as output. The only input is what pieces are on the board and where. So, you can see it as the programmers enforcing this rule: the value of a position depends on which pieces are placed where. This is what the AI "knew" as ...


7

I don't have enough reputation to comment, but AlphaGo Zero Explained In One Diagram is pretty good. I also really like this tutorial. Note that the first link doesn't describe when to create (expand) nodes. That part can be a little confusing. This link may help.


7

Google's hardware is already very convincing. However, allowing a network running forever doesn't mean it'll play stronger chess. There is always limitation, in machine learning we say the network has reached "convergence". Google developers must eventually stop the training, and evaluate it's performance. They would make a better model in the next ...


7

+28, =72, -0 corresponds to a score of 64%. The FIDE Rating Regulations effective from 1 July 2017 give details for calculating rating differences in table 8.1a. According to that table a fractional score of 0.64 corresponds to a rating difference of 102. Hence if Stockfishes rating is 3378 then AlphaZero's is 3378+102 = 3480


6

This is an incredibly interesting time to be alive. Chess computers starting from the 1970s have been minimax-tree based search algorithms using alpha-beta pruning. These programs got stronger and stronger both because of advances in computer speed and parallelism and because of improvements in the heuristic eval function used to prune branches and select ...


6

The LC0 authors studied the AlphaZero paper very carefully, ran their own experiments, and they came to the following conclusion. AlphaZero, despite calling it's algorithm Monte Carlo tree search (All Monte Carlo methods are by definition explicitly random), does not employ any explicit non-determinism after a certain number of moves (I believe this is 15 ...


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