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[Bug-gnubg] Variance reduction efficiency

From: Philippe Michel
Subject: [Bug-gnubg] Variance reduction efficiency
Date: Thu, 24 Aug 2017 22:28:54 +0200 (CEST)
User-agent: Alpine 2.21 (BSF 202 2017-01-01)

On Thu, 24 Aug 2017, tchow wrote:

O.K., so let me rephrase my suggestion: What happens if we use n-ply variance reduction for an n-ply rollout, at least for the first or second steps of a rollout trial?

I don't have an answer to this specific question, but some (not statistically significant) data may give an idea.

Rolling out some middle-game position at various plies gave (VR vs. no-VR) :

At 0-ply (VR at 0-ply) :
duration : x 21.3, SD : / 6.6, equivalent number of trials : x 44

At 1-ply (VR at 0-ply) :
duration : +45%, SD : / 6.4, equivalent number of trials : x 41

At 2-ply (VR at 1-ply) :
duration : +4.5%, SD : / 13.2, equivalent number of trials : x 174

At 3-ply (VR at 2-ply) :
duration : +3.7%, SD : / 17.4, equivalent number of trials : x 301

So, a higher ply for variance reduction helps (although the returns are diminishing with higher plies). On the other hand, using the same ply as the rollout itself, while better than no VR, is extremely expensive.

With your proposal used for the usual 2-ply rollouts the first few steps would be 20 times slower, the following ones unchanged. The total number of steps would depend of the position but the final cost may be in the x 1.5 to x 2 range, similar to the gain in accuracy when *all* steps use 2-ply variance reduction.

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