We study content caching in a wireless network in which the users are connected through a base station that is equipped with a finite-capacity cache. We assume a fixed set of contents whose popularity varies with time. Users' requests for the content depend on their instantaneous popularity levels. Proactively caching contents at the base station incurs a cost but not having requested contents at the base station also incurs a cost. We propose to proactively cache contents at the base station so as to minimize content missing and caching costs. We formulate the problem as a discounted cost Markov decision problem that is a restless multi-armed bandit problem. We provide conditions under which the problem is indexable and also propose a novel approach to maneuver a few parameters to render the problem indexable. We demonstrate the efficacy of the Whittle index policy via numerical evaluation.

翻译：我们研究无线网络中的内容缓存问题，其中用户通过配备有限容量缓存的基站进行连接。假设固定内容集合的流行度随时间动态变化，用户对内容的请求取决于其瞬时流行程度。在基站主动缓存内容会产生成本，而未将请求内容缓存于基站同样会导致成本。我们提出在基站实施主动缓存策略，以最小化内容缺失成本与缓存成本之和。该问题被建模为折扣成本马尔可夫决策问题，本质属于休眠多臂强盗问题。我们给出了问题满足索引性（indexability）的条件，并提出通过调控若干参数使问题具备索引性的创新方法。数值评估结果验证了Whittle索引策略的有效性。