[Computer-go] parameter optimization (clop & others)

Olivier Teytaud olivier.teytaud at lri.fr
Thu Feb 7 04:00:03 PST 2013

 as many of you I guess, I often try to optimize parameters of strategies.

In games, if I optimize against a fixed opponent, this is a noisy
optimization problem: I want the parameters with the best success rate
against the chosen opponent,
which can be evaluated thanks to repeated (time-consuming) games.

The state of the art in noisy optimization is slightly unreadable.

For most tools there are properties such as
   << log( distance to optimum ) ~ - C log( number of evaluations) >>
   for some positive C.

In some cases, C=1/2 (or something close to 1/2 depending on derivability
conditions), but this is restricted to easy problems.

For other families of functions and under some technical assumptions aimed
at getting rid of too simple objective functions,
Basically, one then get rates such as C=1/4, for a quadratic objective
function. However, the bounds are C<=1/2, so there is still a gap.

So basically one can get nearly any result depending on the assumptions :-)

I'd like to know which rates you get on your favorite optimization
problems. Maybe many people here don't care about noisy optimization
from a maths point of view, but I'm pretty sure that people here work on
real noisy optimization problem and if they plot curves such as the equation
above it will provide interesting information.

Thanks for any feedback :-)

Best regards,
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