标题： 高维线性上下文老虎机中的稀疏性导航 显示英文标题

标题： Navigating Sparsities in High-Dimensional Linear Contextual Bandits

摘要： 高维线性上下文老虎机问题由于维度灾难仍然是一项重大挑战。 现有方法通常考虑模型参数是稀疏的，或者上下文协方差矩阵的特征值是（近似）稀疏的，由于传统奖励估计器的刚性，缺乏普遍适用性。 为克服这一限制，本文引入了一种强大的逐点估计器，该估计器可以自适应地遍历这两种稀疏性。 基于此逐点估计器，提出了一种新的算法，称为HOPE。 理论分析表明，HOPE不仅在之前讨论的同质设置中实现了改进的遗憾界限（即仅考虑一种类型的稀疏性），而且首次有效地处理了两种新的具有挑战性的异质设置（即考虑两种类型的稀疏性的混合），突显了其灵活性和普遍性。 实验验证了HOPE在各种场景下优于现有方法。 显示英文摘要

摘要： High-dimensional linear contextual bandit problems remain a significant challenge due to the curse of dimensionality. Existing methods typically consider either the model parameters to be sparse or the eigenvalues of context covariance matrices to be (approximately) sparse, lacking general applicability due to the rigidity of conventional reward estimators. To overcome this limitation, a powerful pointwise estimator is introduced in this work that adaptively navigates both kinds of sparsity. Based on this pointwise estimator, a novel algorithm, termed HOPE, is proposed. Theoretical analyses demonstrate that HOPE not only achieves improved regret bounds in previously discussed homogeneous settings (i.e., considering only one type of sparsity) but also, for the first time, efficiently handles two new challenging heterogeneous settings (i.e., considering a mixture of two types of sparsity), highlighting its flexibility and generality. Experiments corroborate the superiority of HOPE over existing methods across various scenarios.