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.
Solving Bernoulli Rank-One Bandits with Unimodal Thompson Sampling
ENS Paris-Saclay（巴黎萨克雷高等师范学院）；CNRS（法国国家科学研究中心）；Université de Lille（里尔大学）；Inria（法国国家信息与自动化研究所）；DeepMind（深度思维）；CentraleSupélec（中央理工-高等电力学院）
随机秩一Bandits（Katarya et al，（2017 a，b））是一个简单的框架，用于在秩一矩阵上的后悔最小化问题。最初提出的算法被证明有对数遗憾，但不符合现有的下限为这个问题。我们首先证明了一级强盗是单峰强盗的一个特殊例子，然后提供了一个新的单峰汤普森采样（UTS）分析，最初由Paladino等人（2017）提出。我们证明了一个渐近最优的遗憾界上的频率后悔的UTS和我们支持我们的主张与模拟显示我们的方法相比，国家的最先进的显着改善。
Thompson sampling for improved exploration in GFlowNets
Mila – Québec AI Institute（米拉-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）；DreamFold（DreamFold公司）；McGill University（麦吉尔大学）；Polytechnique Montréal（蒙特利尔理工学院）
GSC-QEMit: A Telemetry-Driven Hierarchical Forecast-and-Bandit Framework for Adaptive Quantum Error Mitigation
1 Department of Software Engineering, Rochester Institute of Technology, Rochester, USA Emails；2 Institute for Quantum \& Information Sciences, Syracuse University, Syracuse, USA Emails
Unimodal Training-Multimodal Prediction: Cross-modal Federated Learning with Hierarchical Aggregation
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Nanjing University（南京大学）；University of California, Irvine（加州大学欧文分校）；The Chinese University of Hong Kong（香港中文大学）
