What does a light-tailed simulated human do to a collaborative robot's timeout?

What it found

A robot that waits for a human and aborts after τ has cost J(τ) = wE[min(T,τ)] + cP(T>τ), with slope S(τ)(w − c·h(τ)). Simulated humans with constant or increasing hazard (exponential, Weibull) therefore have only corner-optimal timeouts and, when aborting costs more than the mean wait, never give up. Against a lognormal human (σ=1.2, an assumed model) the interior optimum is 9.4 s and the light-tailed twin’s regret is 3.7% of the optimum, rising to 37% (σ=1.6) and 81% (σ=2) for heavier tails and cheap aborts. A lognormal twin with the right mean and σ off by 0.2 recovers all but 0.5%. Fitting the correct family from n real trials costs regret ∝ 1/n, matched by the delta method to within 11% (0.0323 at n=10, 0.00034 at n=1000). Stylised: scalar i.i.d. response time, one fixed timeout, no real human data.

A figure from its own output

Paper, code and results

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

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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.