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Thompson Algorithm and Multi-armed Bandit Problem

Farazmand, Siavash | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53891 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Haji Mirsadeghi, Miromid; Alishahi, Kasra; Zamani, Sadegh
  7. Abstract:
  8. The multi-armed bandit problem is a popular model for studying exploration/exploitation trade-off in sequential decision problems. Many algorithms are now available for this well-studied problem. One of the earliest algorithms, given by W. R. Thompson, dates back to 1933. This algorithm,referred to as Thompson Sampling, is a natural Bayesian algorithm. The basic idea is to choose an arm to play according to its probability of being the best arm. Thompson Sampling algorithm has experimentally been shown to be close to optimal. In this dissertation several papers are being reviewed. In these papers it has been shown that Thompson Sampling algorithm achieves logarithmic expected regret for the stochastic multi-armed bandit problem. Moreover, a variant of Thompson sampling is being discussed. This variant is used for nonparametric reinforcement learning in a countable classes of general stochastic environments. It has been shown that Thompson sampling is close to optimal in this general setting. Finally, a multi-armed bandit algorithm that explores based on randomizing its history is being discussed. This algorithm estimates the value of an arm from the bootstrap sample of its history. The advantage with this idea, is that it can be used for any reward signal
  9. Keywords:
  10. Multi-Armed Bandit Problem ; Reinforcement Learning ; Thompson Algorithm

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