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article · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2025

Identification of the Strongest Die in Dueling Bandits

Shang Lu, Kohei Hatano, Shuji Kijima, Eiji Takimoto

Cited by 0Open access

Abstract

This work introduces the dueling dice problem, which is a variant of the multi-armed dueling bandit problem. A die is a set of m arms in this problem, and the goal is to find the best set of m arms from n arms (m ≤ n) by an iteration of dueling dice. In a round, the learner arbitrarily chooses two dice α ⊆ [n] and β ⊆ [n] and lets them duel, where she roles dice α and β, observes a pair of arms i ∈ α and j ∈ β, and receives a probabilistic result Xi,j ∈ {0,1}. This paper investigates the sample complexity of an identification of the Condorcet winner die, and gives an upper bound O(nh-2(log log h-1 + log nm2γ-1)m log m) where h is a gap parameter and γ is an error parameter. Our problem is closely related to the dueling teams problem by Cohen et al. 2021. We assume a total order of the strength over arms similarly to Cohen et al. 2021, which ensures the existence of the Condorcet winner die, but we do not assume a total order of the strength over dice unlike Cohen et al. 2021.

Cite this paper

APA 7

Lu, S., Hatano, K., Kijima, S., & Takimoto, E. (2025). Identification of the Strongest Die in Dueling Bandits. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, E108.A(8), 1026–1033. https://doi.org/10.1587/transfun.2024eap1078

MLA 9

Lu, Shang, et al. “Identification of the Strongest Die in Dueling Bandits.” IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, vol. E108.A, no. 8, 2025, pp. 1026–33, https://doi.org/10.1587/transfun.2024eap1078.

Chicago

Lu, Shang, Kohei Hatano, Shuji Kijima, and Eiji Takimoto. 2025. “Identification of the Strongest Die in Dueling Bandits.” IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences E108.A (8): 1026–33. https://doi.org/10.1587/transfun.2024eap1078.

Harvard

Lu, S. et al. (2025) ‘Identification of the Strongest Die in Dueling Bandits’, IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, E108.A(8), pp. 1026–1033. Available at: https://doi.org/10.1587/transfun.2024eap1078.

BibTeX
@article{lu2025identification,
  title = {{Identification of the Strongest Die in Dueling Bandits}},
  author = {Lu, Shang and Hatano, Kohei and Kijima, Shuji and Takimoto, Eiji},
  journal = {IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences},
  volume = {E108.A},
  number = {8},
  pages = {1026--1033},
  year = {2025},
  doi = {10.1587/transfun.2024eap1078}
}

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