Heuristic Solutions for the Best Secretary Problem

Abstract: This paper introduces a heuristic framework for the Best Secretary Problem, where one item must be selected using rank information only. We develop five data-responsive rules extending classical fixed-cutoff methods: an expected-record threshold, an adaptive deviation correction, a probabilistic early-accept rule, a two-phase relaxation, and a local dynamic programming approximation. These rules adjust thresholds sequentially as information accumulates. Simulations across diverse sample sizes, distributions, and autocorrelated settings show that the heuristics match or exceed traditional optimal rules in stability and efficiency. The expected-record rule remains strong despite its simplicity, the adaptive correction performs well under asymmetry, and the adaptive and probabilistic rules reduce average stopping times. An ensemble combining multiple rules yields the most stable performance. Overall, a few intuitive parameters achieve near-optimal results, demonstrating that data-responsive heuristics can effectively extend rank-based optimal stopping to dynamic decision environments.