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Comment by thomasahle | Hacker News Reader

Logistic regression can learn some quite amazing things. I trained a linear function to play chess: https://github.com/thomasahle/fastchess and it manages to predict the next moves of top engine games with 27% accuracy.

A benefit of logistic regression is that the resulting model really fast. Furthermore, it's linear, so you can do incremental updates to your prediction. If you have `n` classes and `b` input features change, you can recompute in `bn` time, rather than doing a full matrix multiplication, which can be a huge time saver.

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Isn't 27% worse than flipping a coin?

A typical chess position has 20-40 legal moves. The complete space of moves for the model to predict from has about 1800 moves.

For comparison Leela Zero gets around 60% accuracy on predicting its own next move.

With this sort of accuracy you can reduce the search part of the algorithm to an effective branching factor of 2-4 rather than 40, nearly for free, which is a pretty big win.

I don’t understand the comment about Leela. Why isn’t own move prediction deterministic?

Because Leela (like fastchess mentioned above) has two parts: A neural network predicting good moves, and a tree search exploring the moves suggested and evaluating the resulting positions (with a second net).

If the prediction (policy) net had a 100% accuracy, you wouldn't need the tree search part at all.

Got it. Thanks for clarifying. Let me restate.

Part one of Leela ranks several chess moves. Part two picks among those.

60% of the time part 2 chooses the #1 ranked move.

That works :-)

One addition: The second part can be run for an arbitrary amount of time, gradually improving the quality of the returned move.

The 60% figure comes from the training games, which are played very quickly, and so don't have a lot of time for refining, thus increasing the prediction accuracy.

In real games, tcec-chess.com/ this "self accuracy" would probably be a bit lower.

You haven’t mentioned any nondeterministic behaviour, therefore Leela is supposed to predict it’s own moves with a 100% accuracy.

It's not non-determinism, it's partial information. The NN part guesses the best move that will be found by search X% of the time. If you just ditched the search part, Leela would be faster and lose out on (1-X)% of the better moves.

Only if you have only two legal moves.

No, uniform random would be bounded by 1/16. However you cannot move ever piece in every configuration, so it's greater than that. Actually would be an interesting problem for figure out...

There are only 16 pieces, but in most board positions, many pieces can make more than one legal move.

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