[Computer-go] PUCT formula

Brian Sheppard sheppardco at aol.com
Fri Mar 9 09:03:17 PST 2018

However, the formula in the AGZ paper doesn't look like any "UCT variant". Formula from paper: Cpuct * P(s,a) * sqrt(Sum(N(s,b))) / (1 + N(s,a)) Note that there is no logarithmic term, and the division by N+1 falls outside the sqrt. For comparison, a normal UCT term looks like sqrt(ln(sum(N(s,b))) / (1 + N))

Since I asked my question, I found that other people have also noticed a discrepancy. I saw a post on a DeepChem board about this subject. I also found a paper (https://webdocs.cs.ualberta.ca/~mmueller/ps/2016/2016-Integrating-Factorization-Ranked.pdf) by our old friends Chenjun Xiao and Martin Muller: 

    "We apply a variant of PUCT [11] formula which is used in AlphaGo [12] to integrate FBT knowledge in MCTS. ...." But then the formula that they give differs: argmax((Q(s,a) + Cpuct * P(s,a) * sqrt( lg(N(s)) / (1 + N(s,a)))

I am guessing that Chenjun and Martin decided (or knew) that the AGZ paper was incorrect and modified the equation accordingly.

Anyone remember anything about this?

-----Original Message-----
From: Computer-go <computer-go-bounces at computer-go.org> On Behalf Of Gian-Carlo Pascutto
Sent: Friday, March 9, 2018 4:48 AM
To: computer-go at computer-go.org
Subject: Re: [Computer-go] PUCT formula

On 08-03-18 18:47, Brian Sheppard via Computer-go wrote:
> I recall that someone investigated this question, but I don’t recall 
> the result. What is the formula that AGZ actually uses?

The one mentioned in their paper, I assume.

I investigated both that and the original from the referenced paper, but after tuning I saw little meaningful strength difference.

One thing of note is that (IIRC) the AGZ formula keeps scaling the exploration term by the policy prior forever. In the original formula, it is a diminishing term.

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