Unverified50% confidenceFactExact time
Under a fixed compute budget, the optimal number of repetitions is N* = sqrt(a * sigma^2 / (b * tau^2)), where sigma^2 is the per-question variance, tau^2 is the per-repetition (resampling) variance, and a and b are cost coefficients.
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10/13/2026
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Related Claims
UnverifiedUnder the AM-GM optimal solution, the product of the minimum achievable variance and the budget equals (sqrt(a*tau^2) + sqrt(b*sigma^2))^2.76% similarUnverifiedFor the balanced target (the uniform distribution over binary strings of even length n containing exactly n/2 ones), the minimum expected number of rounds required as measured by scheduling-averaged divergence is Θ_ε((log n)^2).62% similarUnverifiedThe load balancing loss uses the sum of squares of all expert selection frequencies L=ΣFi², and by the Cauchy–Schwarz inequality the loss is minimized when all Fi=1/N.61% similarUnverifiedThe optimal number of repetitions depends only on the ratio of the per-question variance to the per-repetition variance, and not on the absolute size of the budget.60% similarUnverifiedWhen the quantile level τ=0.5, quantile loss degenerates to Mean Absolute Error (MAE).59% similar
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