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
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