How many retries does a grasp need when the simulator treats attempts as independent?

What it found

A pick skill is retried until success. The twin draws attempts independently at p = 0.6; in the “real” system each object has a latent success probability (Beta, same mean), so single-attempt validation cannot tell them apart while attempts on one object are correlated. Real failure after k attempts is exactly ∏(b+j)/(a+b+j), a power law k^−a against the twin’s geometric law (matched to simulation). At the twin’s 6-attempt budget for δ = 0.01 (claimed 0.004) real failure is 0.010, 0.042 or 0.151 at correlation 0.05, 0.2 or 0.5, and the budget actually needed is 7, 13 or 571. The payoff cost of a wrong budget is mostly small (0–6%, 23% in one case) because the optimal give-up rule is closed-form. Two forced attempts per object identify the correlation, but a budget aimed at δ still needs a safety margin (met in 51–79% of repeats). 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

• How optimistic is the best of K controllers chosen in a noisy digital twin?The best of K controllers picked in a noisy twin: winner's claim optimistic by exactly τ²c_K/√(v²+τ²) (c_K=E max of K normals), under a fixed rollout budget more candidates can make the deployed one worse (best K=5–22), an exact-plant LQ twin's claim falls below what any gain can achieve, and screen-then-verify cuts claim bias 4.5×.
• How many real rollouts does a biased digital twin save when evaluating a robot policy?Evaluating a robot policy with a biased twin as a control variate: unbiased whatever the twin's bias (+0.700 twin-only vs +0.001), exact variance σ²((1−ρ²)/n+ρ²/N), ρ=η for a faithful twin but √η for a noise-free one (1.33× vs 2.0× real-sample gain), worth-it threshold c_T/c_R<(1−√(1−ρ²))²/ρ² (0.072 at ρ=0.5), and 86–125 vs 164 real episodes per policy to rank correctly when twin bias favours the wrong one.
• How big a pilot decides whether a biased digital twin is worth using?How big a pilot decides whether a biased twin is worth using: threshold ρ*=2√r/(1+r) with a gain linear in ρ−ρ*, so wrong calls are frequent but cheap (regret 0.004–0.016 at ρ=0.5), decision-regret law f·slope·(1−ρ*²)²/(2m) (ratio 0.63→1.00 for m=10→160), plug-in allocation ≈0.27–0.30/m, and an adaptive two-stage design that stays unbiased (|bias| ≤ 0.002) with 0.946–0.955 coverage.
• Does giving two policies the same seed in a digital twin actually pair them?Seed-paired (common random numbers) policy comparison in a twin: correlation is exactly lost to random-stream desynchronisation (flat score 0.95→0.77, terminal score 0.36→0.001 at q=0.05→0.3), a sizing trap (power 0.11–0.85 vs nominal 0.90), and counter-keyed draws restore ρ=1.
• What overshoot does a controller tuned in a fixed-step digital twin really have?What overshoot a controller tuned in a fixed-step twin really has: exact per-step decay laws for explicit/semi-implicit/implicit Euler, damping bias flips sign at ζ=1/√2 (explicit, implicit), a 10% twin target delivers 0.105–0.192 real overshoot (implicit/semi-implicit) or 0.036–0.091 (explicit), error first order in h, Richardson repair.
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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.