Efficient and Adaptive Posterior Sampling Algorithms for Bandits

• URL: http://arxiv.org/abs/2405.01010v1
• Date: Thu, 2 May 2024 05:24:28 GMT
• Title: Efficient and Adaptive Posterior Sampling Algorithms for Bandits
• Authors: Bingshan Hu, Zhiming Huang, Tianyue H. Zhang, Mathias Lécuyer, Nidhi Hegde,
• Abstract summary: We study Thompson Sampling-based algorithms for bandits with bounded rewards. We propose two parameterized Thompson Sampling-based algorithms. Both algorithms achieve $O left(Klnalpha+1(T)/Delta right)$ regret bound, where $K$ is the number of arms, $T$ is the finite learning horizon, and $Delta$ denotes the single round performance loss when pulling a sub-optimal arm.
• Score: 5.050520326139362
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study Thompson Sampling-based algorithms for stochastic bandits with bounded rewards. As the existing problem-dependent regret bound for Thompson Sampling with Gaussian priors [Agrawal and Goyal, 2017] is vacuous when $T \le 288 e^{64}$, we derive a more practical bound that tightens the coefficient of the leading term %from $288 e^{64}$ to $1270$. Additionally, motivated by large-scale real-world applications that require scalability, adaptive computational resource allocation, and a balance in utility and computation, we propose two parameterized Thompson Sampling-based algorithms: Thompson Sampling with Model Aggregation (TS-MA-$\alpha$) and Thompson Sampling with Timestamp Duelling (TS-TD-$\alpha$), where $\alpha \in [0,1]$ controls the trade-off between utility and computation. Both algorithms achieve $O \left(K\ln^{\alpha+1}(T)/\Delta \right)$ regret bound, where $K$ is the number of arms, $T$ is the finite learning horizon, and $\Delta$ denotes the single round performance loss when pulling a sub-optimal arm.

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