🤖 AI Summary
This paper addresses the classical secretary problem—online selection of the best candidate based solely on relative rank information. To overcome the poor adaptability of conventional fixed-threshold policies, we propose a data-responsive heuristic framework featuring sequential threshold adaptation. It integrates five tunable rules—including expected-record thresholds, adaptive bias correction, and probabilistic early-stopping—and employs two-stage relaxation with local dynamic programming approximation to enhance robustness and decision efficiency. The method synergistically combines probabilistic modeling with lightweight ensemble learning. Extensive simulations across diverse scenarios validate its efficacy. Experimental results show that the framework achieves near-optimal performance with minimal intuitive hyperparameters, consistently outperforming classical strategies in both average-case performance and stability; the ensemble variant demonstrates the highest robustness.
📝 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.