针对高斯奖励的分簇多臂问题，提出更优的在线学习算法。
Fast Online Learning with Gaussian Prior-Driven Hierarchical Unimodal Thompson Sampling
- 利用两级分层结构设计分簇贝叶斯采样策略
- 理论证明可降低累计后悔值，优于传统方法
- 适合有分簇或单峰奖励结构的实时决策场景
我们研究一类具有高斯奖励反馈的多臂老虎机问题，其中各臂存在聚集特性。此类设置在毫米波通信和风险资产投资组合管理等实际场景中具有广泛应用，源于高斯分布的普遍性。基于带高斯先验的汤普森采样（TSG）算法，我们提出了专为两级分层结构设计的分簇高斯先验汤普森采样（TSCG）。理论上证明，利用该分层结构可获得比标准TSG更低的后悔上界。进一步地，当奖励呈单峰分布时，我们提出的单峰分簇高斯先验汤普森采样（UTSCG）算法可实现更低的后悔上界。所有算法均提供理论后悔上界分析，数值实验验证了其性能优势。
原文摘要 · Abstract (English)
We study a type of Multi-Armed Bandit (MAB) problems in which arms with a Gaussian reward feedback are clustered. Such an arm setting finds applications in many real-world problems, for example, mmWave communications and portfolio management with risky assets, as a result of the universality of the Gaussian distribution. Based on the Thompson Sampling algorithm with Gaussian prior (TSG) algorithm for the selection of the optimal arm, we propose our Thompson Sampling with Clustered arms under Gaussian prior (TSCG) specific to the 2-level hierarchical structure. We prove that by utilizing the 2-level structure, we can achieve a lower regret bound than we do with ordinary TSG. In addition, when the reward is Unimodal, we can reach an even lower bound on the regret by our Unimodal Thompson Sampling algorithm with Clustered Arms under Gaussian prior (UTSCG). Each of our proposed algorithms are accompanied by theoretical evaluation of the upper regret bound, and our numerical experiments confirm the advantage of our proposed algorithms.
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