Probability · Maths EE idea · Ambitious
When to stop looking: the secretary problem
A research question to start from
Why is rejecting the first n/e candidates the optimal stopping rule in the secretary problem, and how robust is the rule when the assumptions change?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
An optimisation in probability with a beautiful limit and assumptions worth questioning.
Mathematics you would need
- Conditional probability
- Sums approximated by integrals
- Optimisation
- Limits
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Derive the success probability for a cut-off rule.
- Optimise and find the limit 1/e.
- Test variants (unknown n, partial ranking information).
Scope and difficulty
Ambitious. Ambitious.
Pitfalls
- Applications to dating or housing taking over.
- No proof of optimality among cut-off rules.
Where to start reading
Search a library catalogue or a university's open lecture notes for: secretary problem optimal stopping 1/e proof. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).