Multi-Armed Exponential Bandit

36 Pages Posted: 2 Dec 2020 Last revised: 14 Feb 2021

See all articles by Kanglin Chen

Kanglin Chen

Hong Kong University of Science & Technology (HKUST) - Dept. of Industrial Engineering and Decision Analytics

Ying-Ju Chen

Hong Kong University of Science & Technology (HKUST) - Department of Information Systems, Business Statistics and Operations Management; Hong Kong University of Science & Technology (HKUST) - Dept. of Industrial Engineering and Decision Analytics

Guillermo Gallego

HKUST

Pin Gao

School of Data Science, The Chinese University of Hong Kong, Shenzhen; Shenzhen Institute of Artificial Intelligence and Robotics for Society

Haoyu Liu

City University of Macau

Date Written: November 3, 2020

Abstract

Exponential bandits are widely adopted in economics and marketing due to their tractability. This paper analyzes the one-agent multi-armed account of exponential bandits, where the agent dynamically selects arms to maximize total payoff. We motivate our base model by examples with arms being of the same type, while the results are generalized to cases where arms are either independent or dependent. The contribution is fourfold. First, we characterize the optimal policy for the agent to choose arms. Under the optimal policy, the agent selects one arm each time, and an arm is used at most once. Second, we show that the agent may not regard information acquisition as a last-ditch effort before quitting, which contradicts the existing literature. Third, with a discount factor, an arm may be used more than once. Fourth, for the case of negatively correlated bandits, the agent may use more than one arms simultaneously. The paper is of both theoretical and practical significance since the model fits well with various situations, including project selection, product promotion, and drug development. Implications for these applications are discussed.

Keywords: multi-armed bandit, experimentation, exponential distribution, information acquisition, project management

Suggested Citation

Chen, Kanglin and Chen, Ying-Ju and Gallego, Guillermo and Gao, Pin and Liu, Haoyu, Multi-Armed Exponential Bandit (November 3, 2020). Available at SSRN: https://ssrn.com/abstract=3724377 or http://dx.doi.org/10.2139/ssrn.3724377

Kanglin Chen

Hong Kong University of Science & Technology (HKUST) - Dept. of Industrial Engineering and Decision Analytics ( email )

Hong Kong

Ying-Ju Chen

Hong Kong University of Science & Technology (HKUST) - Department of Information Systems, Business Statistics and Operations Management ( email )

Clear Water Bay
Kowloon
Hong Kong

Hong Kong University of Science & Technology (HKUST) - Dept. of Industrial Engineering and Decision Analytics ( email )

Hong Kong

Guillermo Gallego

HKUST ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

HOME PAGE: http://https://seng.ust.hk/about/people/faculty/guillermo-gallego

Pin Gao (Contact Author)

School of Data Science, The Chinese University of Hong Kong, Shenzhen ( email )

Shenzhen Institute of Artificial Intelligence and Robotics for Society ( email )

Haoyu Liu

City University of Macau ( email )

87 號, 81 Av. Xian Xing Hai
Macau
China

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