How do you estimate a controller's real-world cost with a biased digital twin?

What it found

A twin-only cost estimate is biased by the twin’s error, a real-only one is noisy; as a control variate the twin keeps the estimate unbiased and is worth its correlation with real rollouts, not its accuracy. Under common disturbances the cost correlation has a closed form and decays as (1+c⁴)/(1−c⁴)²(kδ)² in the twin’s gain error (0.985, 0.941, 0.782, 0.472 for gains 1.15, 1.3, 1.6, 2.0 while the twin-only bias grows 0.004 to 1.34); replaying only a fraction λ of the real disturbance multiplies it by exactly λ². The optimal twin-to-real rollout ratio is √(c_rρ²/(c_t(1−ρ²))), the twin pays only below price (1−√(1−ρ²))²/ρ², and a simulated estimator cut variance to 0.228 of real-only against 0.225 predicted. Twin-only wins at tiny budgets or tiny bias; the control variate is best elsewhere. Stylised.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Digital twins & sim-to-real

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• Can a DiLoCo-style run hide its synchronisation by applying the outer update rounds late?Overlapping the DiLoCo sync by applying the outer step τ rounds late does not pay: stable iff αs < 2 sin(π/(4τ+2)), best rate 1−2 sin(π/(4τ+2))/κ_H (exactly κ_H/(κ_H+1) at τ=1), momentum is useless once τ≥1 (69 → 1388 rounds at κ_H=100), hidden-sync gain ≤ (τ+1) sin(π/(4τ+2)) ≤ 1 (search: 1.5–4.9× slower than blocking averaging), fixed if the fresh pseudo-gradient has weight >½.
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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.