[Computer-go] A Linear Classifier Outperforms UCT on 9x9 Go

Brian Sheppard sheppardco at aol.com
Wed Jun 29 10:17:50 PDT 2011

```Why is a classifier better than having a lookup table indexed by
OurLastMove, OppLastMove, ProposedNextMove that returns the Wins / Trials
experienced when ProposedNextMove is played after the sequence OurLastMove,
OppLastMove?

Are the training cases for your classifier selected from only the UCT nodes,
or also from playout nodes?

Is the output of your classifier used to initialize the Wins / Trials values
for legal moves in new UCT nodes? Is that done by assuming a fixed number of
trials (how many?) and setting Wins = ClassifierOutput * Trials?

Is that the only use of the classifier in the system?

From: computer-go-bounces at dvandva.org
[mailto:computer-go-bounces at dvandva.org] On Behalf Of Peter Drake
Sent: Wednesday, June 29, 2011 11:20 AM
To: computer-go at dvandva.org
Subject: Re: [Computer-go] A Linear Classifier Outperforms UCT on 9x9 Go

On Jun 28, 2011, at 9:39 PM, Imran Hendley wrote:

Hi, long-time lurker and occasional poster here,

Thank you for the paper. I hope you don't mind me asking a few very basic
questions, since I am having trouble understanding exactly what you are
doing.

Let's say we are using a linear classifier. Then our output (the predicted
move) should look like:

argmax_i (y[i]), where y[i] = w1[i] . m1 + w2[i] . m2 + b

Where each w[i] is a weight vector for location i on the board, the m's are
the (column) input vectors (which I assume are 1 at the move location and
zero elsewhere), and b is the bias term.

There is a separate bias for each move, so b in your formula should be b[i].

To train our classifier online, we want to do something like: (1) Generate a
prediction for a training example. (2) Calculate the error. (3) Update the
feature weights. (4) Repeat.

If I understand, online training happens during the course of one game, as
we are playing. Moreover, we are using our classifier to generate moves to
select in the first phase of our simulation, as a replacement for MCTS, and
before playouts.

Correct.

Now this is where I have to start guessing the details. Are our training
examples playouts, and is our error function just 0 if the playout wins, and
1 if it loses?

The "correct output" is 1 if the playout wins, 0 if it loses. The error is
the difference between the correct output and the actual output.

And as we run more playouts, the classifier will update its weights and
select a different sequence of moves in the first phase of our simulation
(analogous to selecting different paths down the search tree based on node
scores in MCTS)? And when we use up our allotted time for one turn we just
return the next move (from the current position) that our classifier
predicts, based on its current weights?

We tried this, but the classifier fluctuates quite a bit. (This is, we
think, a desirably property to keep up exploration.) Instead, we choose as
the actual move the move through which the most playouts were played.)

The paper says we fix the number of moves we select with the classifier
before running playouts (unlike starting from the root and expanding in
MCTS). This is where things start getting really fuzzy for me. Do we
propagate the results of a playout back up this sequence? i.e. if we get a
win, do we perform updates of our classifier for each two-move sequence in
the full sequence?

Yes. The classifier therefore learns from the entire playout, not just from
moves generated by the playout. (This is vaguely analogous to RAVE.)

I would really like to get to the deeper questions about interpreting what
is really going on, but I first need to make sure I am on the right page
here. Sincere apologies for the stupid questions. I really hope my
understanding didn't get derailed so early on that most of my questions in
this message are gibberish. But I did want to show that I actually made a
concerted effort to understand the paper before asking what on earth it is

No problem -- we look forward to any insights you can offer!

Peter Drake

http://www.lclark.edu/~drake/

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