The Best-or-Worst and the Postdoc problems with random number of candidates

Bayón, L.; Fortuny, P.; Grau, J. M.; Oller-Marcén, Antonio M.; Ruiz, M. M.

doi:10.1007/s10878-018-0367-6

Cited by 8 publications

(3 citation statements)

References 18 publications

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“…The secretary problem was first introduced by Martin Gardner back in 1960 [34]. The classical secretary problem focuses on the selection of a secretary from a pool of candidates adhering to the following rules [34] [35]:…”

Section: B Secretary Problemmentioning

confidence: 99%

Budgeted Online Selection of Candidate IoT Clients to Participate in Federated Learning

Mohammed

Tabatabai

Al-Fuqaha

et al. 2021

IEEE Internet Things J.

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Machine Learning (ML), and Deep Learning (DL) in particular, play a vital role in providing smart services to the industry. These techniques however suffer from privacy and security concerns since data is collected from clients and then stored and processed at a central location. Federated Learning (FL), an architecture in which model parameters are exchanged instead of client data, has been proposed as a solution to these concerns. Nevertheless, FL trains a global model by communicating with clients over communication rounds, which introduces more traffic on the network and increases the convergence time to the target accuracy. In this work, we solve the problem of optimizing accuracy in stateful FL with a budgeted number of candidate clients by selecting the best candidate clients in terms of test accuracy to participate in the training process. Next, we propose an online stateful FL heuristic to find the best candidate clients. Additionally, we propose an IoT client alarm application that utilizes the proposed heuristic in training a stateful FL global model based on IoT device type classification to alert clients about unauthorized IoT devices in their environment. To test the efficiency of the proposed online heuristic, we conduct several experiments using a real dataset and compare the results against state-of-the-art algorithms. Our results indicate that the proposed heuristic outperforms the online random algorithm with up to 27% gain in accuracy. Additionally, the performance of the proposed online heuristic is comparable to the performance of the best offline algorithm.

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Section: B Secretary Problemmentioning

confidence: 99%

Budgeted Online Selection of Candidate IoT Clients to Participate in Federated Learning

Mohammed

Tabatabai

Al-Fuqaha

et al. 2021

IEEE Internet Things J.

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show abstract

“…The classical Secretary problem has been generalized in many directions [2,3,4,6,9,10,13,15,14,17,18,20,21,23,24,26], including the Prophet inequality model. One such generalization, the Dowry problem (with multiple choices), introduced by Gilbert and Mosteller [15], assumes that one is given a total of s opportunities to select the best applicant, where s ≥ 1.…”

Section: Introductionmentioning

confidence: 99%

A combinatorial proof for the secretary problem with multiple choices

Liu¹,

Milenković²,

Moustakides³

2023

Preprint

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The Secretary problem is a classical sequential decision-making question that can be succinctly described as follows: a set of rank-ordered applicants are interviewed sequentially for a single position. Once an applicant is interviewed, an immediate and irrevocable decision is made if the person is to be offered the job or not and only applicants observed so far can be used in the decision process. The problem of interest is to identify the stopping rule that maximizes the probability of hiring the highest-ranked applicant. A multiple choice version of the Secretary problem, known as the Dowry problem, assumes that one is given a fixed integer budget for the total number of selections allowed to choose the best applicant. It has been solved using tools from dynamic programming and optimal stopping theory. We provide the first combinatorial proof for a related new query-based model for which we are allowed to solicit the response of an expert to determine if an applicant is optimal. Since the selection criteria differ from those of the Dowry problem we obtain nonidentical expected stopping times.Our result indicates that an optimal strategy is the (a s , a s−1 , . . . , a 1 )-strategy, i.e., for the i th selection, where 1 ≤ i ≤ s and 1 ≤ j = s + 1 − i ≤ s, we reject the first a j applicants, wait until the decision of the (i − 1) th selection (if i ≥ 2), and then accept the next applicant whose qualification is better than all previously appeared applicants. Furthermore, our optimal strategy is right-hand based, i.e., the optimal strategies for two models with s 1 and s 2 selections in total (s 1 < s 2 ) share the same sequence a 1 , a 2 , . . . , a s1 when it is viewed from the right. When the total number of applicants tends to infinity, our result agrees with the thresholds obtained by Gilbert and Mosteller.

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“…Section 2 is dedicated to the main result. The long Section 3 is devoted to applying our methodology to several variants of the secretary problem, all of them well-known, in a unified way: the original secretary problem [13,17], the postdoc variant [1,26,28,29], the best-or-worst version [1,2], the secretary problem with uncertain employment [25], the secretary problem with interview cost [5], the win-lose-or-draw marriage problem [10], the duration problem [9], the multicriteria secretary problem [16], and the secretary problem with a random number of applicants [21,22]. Section 4 also includes applications of the new methodology, but now to other problems created ad hoc such as lotteries with increasing prize, the secretary problem with wildcard, the secretary problem with random interruption of the interviews, and the secretary problem with penalty if the second best is selected.…”

Section: Introduction Optimal Stopping Problemsmentioning

confidence: 99%

A new method for computing asymptotic results in optimal stopping problems

Bayón¹,

Fortuny²,

Grau³

et al. 2022

Preprint

Self Cite

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In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold, and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order linear differential equation, makes it possible to systematically obtain these values in many situations. As an example, we address nine variants of the well-known secretary problem, including the classical one, that appear in the literature on the subject, as well as four other unpublished ones.

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The Best-or-Worst and the Postdoc problems with random number of candidates

Cited by 8 publications

References 18 publications

Budgeted Online Selection of Candidate IoT Clients to Participate in Federated Learning

Budgeted Online Selection of Candidate IoT Clients to Participate in Federated Learning

A combinatorial proof for the secretary problem with multiple choices

A new method for computing asymptotic results in optimal stopping problems

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