Taking advantage of contextual information can potentially boost the performance of recommender systems. In the era of big data, such side information often has several dimensions. Thus, developing decision-making algorithms to cope with such a high-dimensional context in real time is essential. That is specifically challenging when the decision-maker has a variety of items to recommend. In addition, changes in items' popularity or users' preferences can hinder the performance of the deployed recommender system due to a lack of robustness to distribution shifts in the environment. In this paper, we build upon the linear contextual multi-armed bandit framework to address this problem. We develop a decision-making policy for a linear bandit problem with high-dimensional feature vectors, a large set of arms, and non-stationary reward-generating processes. Our Thompson sampling-based policy reduces the dimension of feature vectors using random projection and uses exponentially increasing weights to decrease the influence of past observations with time. Our proposed recommender system employs this policy to learn the users' item preferences online while minimizing runtime. We prove a regret bound that scales as a factor of the reduced dimension instead of the original one. To evaluate our proposed recommender system numerically, we apply it to three real-world datasets. The theoretical and numerical results demonstrate the effectiveness of our proposed algorithm in making a trade-off between computational complexity and regret performance compared to the state-of-the-art.

翻译：利用上下文信息可以潜在提升推荐系统的性能。在大数据时代，这类辅助信息通常具有多个维度。因此，开发能够实时处理此类高维上下文的决策算法至关重要。当决策者面临大量可推荐项目时，这一挑战尤为突出。此外，项目流行度或用户偏好的变化，可能因对环境分布变化缺乏鲁棒性而损害部署推荐系统的性能。本文基于线性上下文多臂老虎机框架来解决这一问题。我们针对具有高维特征向量、大量臂集以及非平稳奖励生成过程的线性老虎机问题，开发了一种决策策略。我们基于汤普森采样的策略通过随机投影降低特征向量的维度，并采用指数递增权重来随时间降低过去观测值的影响。所提出的推荐系统利用该策略在线学习用户的物品偏好，同时最小化运行时间。我们证明了一个遗憾界，其缩放因子为降维后的维度而非原始维度。为数值评估所提出的推荐系统，我们将其应用于三个真实世界数据集。理论及数值结果表明，与现有先进方法相比，我们的算法在计算复杂度与遗憾性能之间实现了有效权衡。