Heuristic Solutions for the Best Secretary Problem

TL;DR

This paper develops and tests new heuristic rules for the Best Secretary Problem, improving decision stability and efficiency across various settings by extending classical methods with adaptive, probabilistic, and dynamic approaches.

Contribution

Introduces five novel data-responsive heuristic rules that extend classical fixed-cutoff methods for the Best Secretary Problem, enhancing performance and stability.

Findings

Heuristic rules match or outperform traditional optimal rules in simulations.

Adaptive and probabilistic rules reduce average stopping times.

Ensemble of rules provides the most stable performance.

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.