We consider a stochastic contextual bandit problem where the dimension $d$ of
the feature vectors is potentially large, however, only a sparse subset of
features of cardinality $s_0 \ll d$ affect the reward function. Essentially all
existing algorithms for sparse bandits require a priori knowledge of the value
of the sparsity index $s_0$. This knowledge is almost never available in
practice, and misspecification of this parameter can lead to severe
deterioration in the performance of existing methods. The main contribution of
this paper is to propose an algorithm that does not require prior knowledge of
the sparsity index $s_0$ and establish tight regret bounds on its performance
under mild conditions. We also comprehensively evaluate our proposed algorithm
numerically and show that it consistently outperforms existing methods, even
when the correct sparsity index is revealed to them but is kept hidden from our
algorithm.

本文提出了一种算法来解决随机上下文赌博机问题，该问题中特征向量的维数可能很大，但仅有一个小的稀疏特征子集会影响奖励函数，该算法可以在不需要先前了解稀疏度的情况下使用，并在温和条件下，确立了性能方面的紧密后悔界限，同时，我们全面评估了我们提出的算法的性能，并表明即使将正确的稀疏度指数暴露给现有方法，但将其保持对我们算法隐藏，我们的算法也能始终优于现有方法。