With noisy scores, does a "beat the record by a margin" rule pick the best candidate more often than the best cutoff?
research/free-secretarymargin
With noisy scores, a rule that must beat the earlier best by a margin raises P(pick the true best) from 0.233 to 0.244 at noise 0.5 and 0.143 to 0.149 at noise 1 (n = 50, fresh-trial test); no gain at noise 2; simulation.
What it found
Simulation (n = 50 candidates, parameters tuned on 8,000 training trials, scored on 60,000 fresh paired trials) of a two-parameter margin rule: skip r−1 candidates, then take the first whose noisy score beats the earlier maximum by at least d. P(pick the true best) rises from 0.2334 to 0.2444 at noise 0.5 (+0.0111, se 0.0014) and from 0.1429 to 0.1491 at noise 1 (+0.0062, se 0.0015); at noise 2 the gain (+0.0018, se 0.0011) is not distinguishable from zero, and with no noise the tuning picks the plain cutoff. One setting, one seed pair, a coarse grid; the Bayes-optimal policy is not computed.
A figure from its own output
Paper, code and results
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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.