# [Computer-go] PUCT formula

Martin Mueller mmueller at ualberta.ca
Fri Mar 9 14:12:49 PST 2018

```I talked to Chenjun just now so this is what we both remember.
The PUCB formula as published in Chris Rosin’s paper actually has an additive knowledge term, and it looks nothing like the two different PUCT variants tried in AlphaGo and our paper.

Chenjun tried an additive term as in Chris’ paper first, and it did not work well for him. Then he tried the “UCT-like” PUCT as in our paper, with the decay term under the square root. This worked well for him. He never tried the AlphaGo formula with the faster decay.

Beyond the published papers, my memory is that many people tried many different combinations of knowledge terms and of decay formulas over time. I have never read any systematic comparison, or any principled argument for which type of decay is “best” for which type of knowledge, and why. It must depend on the quality of knowledge, amongst many other things.

There are also earlier MoGo papers that combined many different evaluation terms into one formula and tested them empirically.

Martin

> 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))
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> 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:
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>     "We apply a variant of PUCT  formula which is used in AlphaGo  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)))
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> I am guessing that Chenjun and Martin decided (or knew) that the AGZ paper was incorrect and modified the equation accordingly.
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