[Computer-go] action-value Q for unexpanded nodes

Gian-Carlo Pascutto gcp at sjeng.org
Wed Dec 6 05:52:25 PST 2017

On 06-12-17 11:47, Aja Huang wrote:
> All I can say is that first-play-urgency is not a significant 
> technical detail, and what's why we didn't specify it in the paper.

I will have to disagree here. Of course, it's always possible I'm
misunderstanding something, or I have a program bug that I'm mixing up
with this.

Or maybe you mean that you expect the program to improve regardless of
this setting. In any case, I've now seen people state here twice that
this is detail that doesn't matter. But practical results suggest otherwise.

For a strong supervised network, FPU=0 (i.e. not exploring all successor
nodes for a longer time, relying strongly on policy priors) is much
stronger. I've seen this in Leela Zero after we tested it, and I've
known it to be true from regular Leela for a long time. IIRC, the strong
open source Go bots also use some form of progressive widening, which
produces the same effect.

For a weak RL network without much useful policy priors, FPU>1 is much
stronger than FPU=0.

Now these are relative scores of course, so one could argue they don't
affect the learning process. But they actually do that as well!

The new AZ paper uses MCTS playouts = 800, and plays proportionally
according to MCTS output. (Previous AGZ had playouts = 1600,
proportional for first 30 moves).

Consider what this means for the search probability outputs, exactly the
thing the policy network has to learn. With FPU=1, the move
probabilities are much more uniform, and the moves played are
consequentially much more likely to be bad or even blunders, because
there are less playouts that can be spent on the best move, even if it
was found.

> The initial value of Q is not very important because Q+U is
> dominated by the U piece when the number of visits is small.

a = Q(s, a) + coeff * P(s,a) * (sqrt(parent->visits) / 1.0f +

Assume parent->visits = 100, sqrt = 10
Assume child->visits = 0
Assume P(s, a) = 0.0027 (near uniform prior for "weak" network)

The right most side of this (U term) is ~1. This clearly does not
dominate the Q term. If Q > 1 (classic FPU) then every child node will
get expanded. If Q = 0 (Q(s, a) = 0) then the first picked child
(largest policy prior) will get something like 10 expansions before
another child gets picked. That's a massive difference in search tree
shape, *especially* with only 800 total playouts.


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