Re: [Bug-gnubg] Rolling out higher SD plays more.

[Christopher Yep]

At 03:39 PM 8/31/2009, bob koca wrote:
> Discussing an idea of rolling out plays with higher SD more often than 
> plays with lower SD Chris Yep wrote:
>
> "4. If a user wishes to rollout a move (selecting all reasonable candidate
> plays) until one play is "best" (to some defined level of statistical
> significance and ignoring all systematic errors that gnubg may make during
> the rollouts), this algorithm will almost always reduce the amount of
> rollout time needed."
>
>  Even taking into account that the games for the plays with higher SD 
> could be taking much longer?
>
> Bob Koca

Oops, I forgot to consider that plays with much higher SD often take much 
longer to rollout (per game/trial).  E.g. if one wants to rollout two plays 
(A and B), if play A has standard error 4 times larger (and variance 4*4 = 
16 times larger) than play B but play A takes 16 times longer to rollout 
(per game/trial, on average), then it's actually optimal (for a fixed 
amount of time) to rollout each play an equal number of times (which is 
what gnubg currently does).

If play A takes longer to rollout than play B, but less than 16 times 
longer, there can be gains from rolling out play A more frequently than 
play B (but play A shouldn't be rolled out 16 times more 
frequently).  Calculating the optimal frequency to rollout each play would 
involve tracking the average amount of time per trial for each play; this 
could get a little messy; in general the overall gains might not be that much.

Chris