Stochastic Scheduling with Priority Classes

Garbe, R.; Glazebrook, K. D.

doi:10.1287/moor.23.1.119

Cited by 10 publications

(3 citation statements)

References 16 publications

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“…Now it is widely studied and frequently applied as a theoretical framework for many other sequential statistical decision problems in market pricing, medical research, and engineering, which are characterized by the trade-off between exploration and exploitation (see e.g. [15], [23], and [32]).…”

Section: Introductionmentioning

confidence: 99%

A confirmation of a conjecture on Feldman’s two-armed bandit problem

2023

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The myopic strategy is one of the most important strategies when studying bandit problems. In 2018, Nouiehed and Ross put forward a conjecture about Feldman’s bandit problem (J. Appl. Prob. (2018) 55, 318–324). They proposed that for Bernoulli two-armed bandit problems, the myopic strategy stochastically maximizes the number of wins. In this paper we consider the two-armed bandit problem with more general distributions and utility functions. We confirm this conjecture by proving a stronger result: if the agent playing the bandit has a general utility function, the myopic strategy is still optimal if and only if this utility function satisfies reasonable conditions.

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Section: Introductionmentioning

confidence: 99%

A confirmation of a conjecture on Feldman’s two-armed bandit problem

2023

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“…Now it is widely studied and frequently applied as a theoretical framework for many other sequential statistical decision problems in market pricing, medical research, and engineering, which characterized by the trade-off between exploration and exploitation (see e.g. [2,3,4]).…”

Section: Introductionmentioning

confidence: 99%

A Confirmation of a Conjecture on the Feldman's Two-armed Bandit Problem

Chen¹,

Lin²,

Zhang³

2022

Preprint

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Myopic strategy is one of the most important strategies when studying bandit problems. In this paper, we consider the two-armed bandit problem proposed by Feldman. With general distributions and utility functions, we obtain a necessary and sufficient condition for the optimality of the myopic strategy. As an application, we could solve Nouiehed and Ross's conjecture for Bernoulli two-armed bandit problems that myopic strategy stochastically maximizes the number of wins.

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“…With this approach, a bandit process is naturally formulated as a Markov decision process, the solution of which is often obtained through stochastic dynamic programming. In addition to the aforementioned applications in business and clinical trials, the bandit model is frequently used as a theoretical framework for many other research problems, including stochastic scheduling, queueing networks, optimal investment and consumption, dynamic assortment design, modern online service, and webpage design …”

Section: Introductionmentioning

confidence: 99%

A Bayesian two‐armed bandit model

Wang

Liang

Porth

2018

Appl Stoch Models Bus & Ind

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A two-armed bandit model using a Bayesian approach is formulated and investigated in this paper with the goal of maximizing the value of a certain criterion of optimality. The bandit model illustrates the trade-off between exploration and exploitation, where exploration means acquiring scientific acknowledge for better-informed decisions at later stages (ie, maximizing long-term benefit), and exploitation means applying the current knowledge for the best possible outcome at the current stage (ie, maximizing the immediate expected payoff). When one arm has known characteristics, stochastic dynamic programming is applied to characterize the optimal strategy and provide the foundation for its calculation. The results show that the celebrated Gittins index can be approximated by a monotonic sequence of break-even values. When both arms are unknown, we derive a special case of optimality of the myopic strategy. KEYWORDS bandit processes, Bayesian method, Gittins index, Markov decision processes, optimal strategy 624

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Stochastic Scheduling with Priority Classes

Cited by 10 publications

References 16 publications

A confirmation of a conjecture on Feldman’s two-armed bandit problem

A confirmation of a conjecture on Feldman’s two-armed bandit problem

A Confirmation of a Conjecture on the Feldman's Two-armed Bandit Problem

A Bayesian two‐armed bandit model

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