[Computer-go] Thoughts about bugs and scalability

Richard B Segal rsegal at us.ibm.com
Mon Jun 20 16:25:21 PDT 2011


Agreed.  I was a bit sloppy in describing the convergence.

A more accurate statement is that my data empirically appears to fit a
geometric series with 0 < r < 1.    A geometric series with 0 < r < 1 is
guaranteed to converge.   Whether Fuego actually converges to an asymptote
depends on how accurately the geometric series models the real-world data.
If you take a look at the paper you will see that the fit between the model
and the empirical data is excellent.   Still, nothing guarantees that the
1) projected trend will continue, and 2) that I have selected the best
curve to fit the data.

- Rich

computer-go-bounces at dvandva.org wrote on 06/20/2011 07:01:57 PM:

> [image removed]
>
> Re: [Computer-go] Thoughts about bugs and scalability
>
> Álvaro Begué
>
> to:
>
> nick, computer-go
>
> 06/20/2011 07:03 PM
>
> Sent by:
>
> computer-go-bounces at dvandva.org
>
> Please respond to computer-go
>
> On Mon, Jun 20, 2011 at 6:00 PM, Nick Wedd <nick at maproom.co.uk> wrote:
> > On 20/06/2011 21:03, Richard B Segal wrote:
> >>
> >> Hi All,
> >>
> >> As my scalability paper has come up several times in the last few
weeks
> >> I thought it would be useful to give a brief overview of the results
> >> relevant to the current conversation and provide additional insights.
> >>
> >> The first set of experiments analyzed the scalability of Fuego on a
> >> single core machine without multithreading. The experiments consisted
of
> >> 1,000 self-play games where one player received N minutes for all
moves,
> >> and the second player receiving 2*N minutes for all moves. The
resulting
> >> scaling graph looks qualitatively similar to the recent scaling graph
> >> posted for Pachi. The important observation is that the ELO gained
> >> between each successive doubling decreases as search time increases.
If
> >> we assume this trend continues, then the ELO gained for each doubling
> >> will converge to zero forcing absolute performance to level off.
> >
> > Just a mathematical niggle here -
> > " ELO gained between each successive doubling decreases as search time
> > increases" does not imply convergence to an asymptote.  An example of a
> > function to illustrate this is log(log(N)).
>
> Yes, I was about to say the same thing. The existence of an asymptote
> is a feature of the model that was chosen to fit the curve (an
> exponential). I am suspicious of this type of extrapolation.
>
> Álvaro.
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