Mathematical problem involving optimal stopping theory
Graphs of probabilities of getting the best candidate (red circles) from n applications, and k/n (blue crosses) where k is the sample size
The secretary problem demonstrates a scenario involving optimal stopping theory[1][2] that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also known as the 37% rule.[3]
The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator gains information sufficient to rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant. If the decision can be deferred to the end, this can be solved by the simple maximum selection algorithm of tracking the running maximum (and who achieved it), and selecting the overall maximum at the end. The difficulty is that the decision must be made immediately.
The shortest rigorous proof known so far is provided by the odds algorithm. It implies that the optimal win probability is always at least (where e is the base of the natural logarithm), and that the latter holds even in a much greater generality. The optimal stopping rule prescribes always rejecting the first applicants that are interviewed and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). Sometimes this strategy is called the stopping rule, because the probability of stopping at the best applicant with this strategy is already about for moderate values of . One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.
^Ferguson, Thomas S. (August 1989). "Who Solved the Secretary Problem?". Statistical Science. 4 (3): 282–289. doi:10.1214/ss/1177012493.
^Hill, Theodore P. (2009). "Knowing When to Stop". American Scientist. 97 (2): 126–133. doi:10.1511/2009.77.126. ISSN 1545-2786. S2CID 124798270. For French translation, see cover story in the July issue of Pour la Science (2009).
^Thomson, Jonny (21 April 2022). "Mathematicians suggest the "37% rule" for your life's biggest decisions". Big Think. Retrieved 6 February 2024.
The secretaryproblem demonstrates a scenario involving optimal stopping theory that is studied extensively in the fields of applied probability, statistics...
options). A key example of an optimal stopping problem is the secretaryproblem. Optimal stopping problems can often be written in the form of a Bellman...
world Firing squad synchronization problem Monkey and banana problemSecretaryproblem Stuart J. Russell, Peter Norvig (2010). Artificial Intelligence:...
and efficiency and minimize the total cost of the assignment. The secretaryproblem can also be called the optimal stopping theory. It focuses heavily...
assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has...
marriage problem may refer to: Assignment problem, consisting of finding a maximum weight matching in a weighted bipartite graph Secretaryproblem, also...
economics, and computer science, the stable marriage problem (also stable matching problem) is the problem of finding a stable matching between two equally...
code are crucial. Allegedly, Johannes Kepler clearly exposed this secretaryproblem to a friend of his at a time when he was trying to make up his mind...
analysis. Optimal stopping Odds algorithm Secretaryproblem Hitting time Stopped process Disorder problem Début theorem Sequential analysis Kallenberg...
sales problems, secretaryproblems, portfolio selection, (one way) search strategies, trajectory problems and the parking problem to problems in online...
scheduling problem List update problem Bandit problemSecretaryproblem Search games Ski rental problem Linear search problem Portfolio selection problem Dynamic...
The Scunthorpe problem is the unintentional blocking of online content by a spam filter or search engine because their text contains a string (or substring)...
Arthur Cayley, who discovered the method while attempting to solve the secretaryproblem. In dynamic programming, a method of mathematical optimization, backward...
information, sometimes referred to as the fourth secretaryproblem, also bears his name: Robbins' problem (of optimal stopping). Robbins was born in New...
The United States secretary of defense (SecDef) is the head of the United States Department of Defense, the executive department of the U.S. Armed Forces...
Secretary (Research) in the Cabinet Secretariat, and is under the authority of the Prime Minister of India without parliamentary oversight. Secretary...
around 2014. The first twenty-one Fleet Problems — labeled with roman numerals as Fleet Problem I through Fleet Problem XXI — were conducted between 1923 and...
The Cyprus problem, also known as the Cyprus conflict, Cyprus issue, Cyprus dispute, or Cyprus question, is an ongoing dispute between the Greek Cypriot...
problem is the electronic equivalent of the El Niño and there will be nasty surprises around the globe. — John Hamre, United States Deputy Secretary of...
Germany is Our Problem is a book written in 1945 by Henry Morgenthau Jr., U.S. Secretary of the Treasury during the administration of Franklin D. Roosevelt...
Indiana) was a statistician and mathematician, known for his work on the secretaryproblem and for the Samuels Conjecture involving a Chebyshev-type inequality...
The United States secretary of homeland security is the head of the United States Department of Homeland Security, the federal department tasked with...
The secretarybird or secretary bird (Sagittarius serpentarius) is a large bird of prey that is endemic to Africa. It is mostly terrestrial, spending most...
Global Information
