Objectively Speaking, Is Magnus a Patzer Compared to StockFish and AlphaZero?

 The team includes at least 3 chess programmers. Matthew Lai, the author of Giraffe and Talkchess member, is one of them. It is maybe for a reason that Giraffe, following the very same approach as Alpha, is rated only around 2400 on single core.

So, what you are saying is that AlphaZero is 3600 because they have someone on their team who has created an engine that reached 2400?

Likewise, the team has no chess player at above amateur level. 

However, the reason Matthew Lai is on the team is that he had tried to produce a chess AI, just one that was 1200 points weaker. 1200 points is not a difference that is achievable by speeding up hardware, even a lot. From articles on this, he was using a much smaller neural network, which even on slower hardware was able to look at about 10% as many nodes as a conventional engine.  (see this article)

However, I would agree that using modest computational resources would have been a huge barrier to the development of AlphaZero. The most demanding phase is the self-learning, and this would have taken months without the fast hardware, rather than 4 hours.

The reason AlphaZero benefits from more computation when playing is simply that its search tree gets bigger. But this search tree had 1000 times fewer nodes than that of Stockfish with the exact hardware each used!

It is the huge hardware that made the difference and not the approach.

Self-learning, self-learning, what do you mean self-learning and AI.

You admit you know nothing about the techniques that AlphaZero used to generate its strength: model-based reinforcement learning, termed "deep reinforcement learning" because the model used is a deep neural network.

I have studied this subject (including watching David Silver's excellent lecture series), and use Sutton's book on the subject.

It is true that AlphaZero uses a lot of processing power to achieve its highest strength in head to head play. However, with 30 times less power it would remain the highest rated engine according to AlphaZero's testing. While restricting AlphaZero's computational power would make the match closer, increasing the computational resource for both AlphaZero and a conventional engine like Stockfish would greatly advantage AlphaZero.

The key reason AlphaZero increases in strength more rapidly with computational resource appears to be that the branching factor of its search tree is smaller, to an extent which compensates enormously for it looking at far, far fewer positions. With the full power of 4 TPUs, AlphaZero was still looking at 1000 times fewer nodes than Stockfish! If its time was reduced by a factor of 30, it would be looking at 30,000 times fewer, and still be stronger!

As a result, when AlphaZero gets more time, its horizon must expand significantly faster than that of Stockfish. This is why not only is it stronger, it also indicates this technology has a permanent edge. 

The nature of the evaluation method is quite simple. It has some sort of representation of the position as an array of numbers which are the inputs to the neural network  - the neural network doesn't know what they mean, it has to work this out from they way the relate to the results of games and to their values on other moves - and a large deep neural network with thousands (not sure how many thousands) of nodes in many layers which take the representation of the board and output a number, the expected score from the position. [I hope I haven't missed some published detail].

How the evaluation method gets built comprises two parts (if my understanding is correct - I am supplementing what is published with general ideas about deep reinforcement learning). The obvious one is when a game ends: the exact value of the position is available, and that can be used to adjust the neural network to improve its evaluations of earlier positions in the direction of the right result. The second one is that when it evaluates a position, if this evaluation is a surprise compared to the evaluation of previous positions, the network is tweaked to make the evaluations of previous positions a bit more in agreement with the later evaluation.

The first form of feedback is basically making the evaluation compatible with the absolute value of clear positions. The second form of feedback is basically making the evaluation compatible with the legal continuations in a position: the reason is that the perfect evaluation of a position is the same as that of a later position reached by perfect play.

I am surprised you would make such a wild claim! Stockfish was running on the most powerful computer I have ever heard of it running on - 64 cores - far stronger than are used in most computer competitions. Given that the hash table was a reasonable size (exactly how near to optimal it was is not clear), the effect of the wrong hash table is the same as a fairly modest shift in the CPU speed and Stockfish's rating was changing very little with CPU speed at that level, it is unlikely that this caused many tens of Elo points harm.

As a result, we can be pretty sure the absolute rating of Stockfish's play was as high as its usual rating.

There is the issue of opening book, but in the period since human openings have been less and less useful to computers which are more than 600 points stronger, this too is an efficiency issue. Modern computer opening books are basically the product of computing time in previous computer games, or self-play.

I would point out that selecting an opening book is a different game to playing chess, and it is a someone dull one, since it is about generating a static book and following it by rote. AlphaZero devoted no time to this. However, when playing Stockfish in the full range of best openings on a second equal playing field (both being assisted or hindered equally), it was much stronger than its adversary.

So, does that mean that there exists a function F(position) = Value which does not depend on 20-deep evaluations of the possible moves from the position?  If so, it would be kind of awesome if Google was to publish what that function was at the current state of AZ.  I am sure it would not be human readable - and just as sure that humans would be able to pick key things out of it.  

You made a good point that I should emphasise: the role of those with knowledge of conventional chess engines in the design of the tree search algorithm of AlphaZero, which has some commonality with all chess engines. While I am no expert on chess engines, a key strength of AlphaZero is that it is better at allocating resources to different branches, and that this is achieved by the quality of the neural network's estimates of the probabilty that each move is best, which comes entirely from self-learning.

1) Alpha is some 300-400 elos weaker than SF on single core, and the very same estimate would probably reproduce if SF has access to a hardware similar to that of Alpha

This is neither accurate based on the data, nor especially interesting, any more than the 100m with one leg tied behind people's back is a particularly interesting athletics event.

2) almost a week after that paper and the results were published, that is, 168 hours later, there is still not a communique from Google they have solved chess,

That really is a very foolish comment.

and even that Alpha has improved by meagre 10 elos.

Why would it need to? It has shown itself to be the best. Fischer did not increase his rating at all after the world championship in 1972, but that did not stop him being the champion (until 1975). Not that AlphaZero-Stockfish was a world championship - rather it was a test of the world's strongest chess software against the world champion program.

Why would one think hardware is relevant to Alpha but irrelevant to SF?

One would not think that, but one would infer that Stockfish was improving a LOT slower with time per move (exactly equivalent to CPU speed) over the entire range of testing. Check the paper. This is why the AlphaZero approach will tend to dominate in the end, as massively parallel hardware becomes as ubiquitous as GPUs now. Google's TPUs are much like GPUs (which are also used in a big way in deep learning to speed up computation), but being designed for deep neural networks especially, they are more suited to purpose than GPUs which exist mainly to run video games fast!

So that, basically, they built a 2800 elo engine, I acknowledge that readily. Only thing I can not understand is why they should have made a publicity out of that?

A rating at chess is how well you can play. Not how well you can play if handicapped in the way some guy demands that you should be handicapped. AlphaZero would be shown not to be the best chess player, not when it is sufficiently handicapped, but when another entity, using whatever hardware it likes, is good enough to beat it. You can postulate that such an entity exists, but it has not been demonstrated.

We saw a good match, that is all, a match we had never witnesses before. But, we could easily witness an even better one, if we match latest dev SF(+40 elo) on the 32 cores vs latest dev on 2000 cores. That would be a significantly better match, with higher quality of games, but only Google can find 2000 cores for SF.

There was reported to be a spinoff of Stockfish running on a large cluster (thousands of nodes) several years back. But I am not sure of the status or accuracy of the company's claims. The website still exists, but seems to be inactive. http://www.chesscluster.com/magneto.html

I don't know how strong Stockfish would get with 30 times more cores (or whatever) but I am not sure it could cope with AlphaZero. But I would be interested to see!

So that, again, good hardware achievement. Google is not known to be lacking in funds.

I need to remind you that you have admitted you have no idea how the software works.

Again, you are making a critical mistake from a chess player's perspective. 

The opening database doesn't just give tactical short cuts,

I certainly did NOT claim that it did. This is what is known as a strawman.

What an opening database does is provide choices of move that are probably good in an absolute sense.

it provides positions that are playable. All of the main lines have been analyzed out far more than 40 ply in critical lines, and the resulting positions have been played countless times, by humans and machines.

They have not been played "countless times". They have been played some finite number of times. Once you get a modest distance into an opening, you may find a few thousand games, a few hundred games and so on. Once it gets any lower, the statistical information becomes so noisy as to be highly questionable. The results of these games provide useful evidence as to the quality of a choice, but this is really just some precomputed spindly branches in the tree of possibilities. If it is a hundred games, it may contain quite a lot of computation - say enough for 10,000 move choices - but this computation is too narrow to be ideal. It is worth a lot as a random sample of the results of imperfect play, but has the potential to be revised with one insight (the number and quality of the games are key to how likely this is).

Opening databases don't just provide a "short cut", they provide a platform for reaching playable positions. The requirements of the opening are different from the requirements of a general middle game, and vastly different from those of an endgame. 

An entity that can see 10 moves further with equal reliability (as is likely to be the case with AlphaZero at full power) can do without 10 moves of opening theory.

In turn-based and correspondence chess, the two games are interlaced in real time, for OTB and live chess, the two are interlaced from one game to another. As you say the generation of an opening book is important to chess engines, as it is human professional chess players (and keen amateurs). However, most chess players would agree that the core skill of a strong chessplayer is finding good moves, and it is a far more interesting one. Opening knowledge is a way to manage with less of that skill.

Note that in 960 chess, this factor virtually vanishes for human players. There is only one game, with no opening theory. For computers, opening theory would be spread 960 times more thinly, which dramatically reduces its significance and usefulness (you can get an impression of how much by going to your chess database and imagining there are 1000 fewer games in it).

I think you’re misunderstanding. Computers can’t even be compared to humans as they don’t play in human rating pools, and they play a fundamentally different type of chess than we do. The idea that Magnus is a patzer I think is also a misunderstanding. He’s extremely strong, given that he has to sit at a board for 6 hours and is a very fallible human and computers don’t and aren’t.