Bayesian Linear Bandits for Large-Scale Recommender Systems

Potentially, taking advantage of available side information boosts the performance of recommender systems; nevertheless, with the rise of big data, the side information has often several dimensions. Hence, it is imperative to develop decision-making algorithms that can cope with such a high-dimensional context in real-time. That is especially challenging when the decision-maker has a variety of items to recommend. 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 context vectors and several arms. Our policy employs Thompson sampling and feeds it with reduced context vectors, where the dimensionality reduction follows by random projection. Our proposed recommender system follows this policy to learn online the item preferences of users while keeping its runtime as low as possible. We prove a regret bound that scales as a factor of the reduced dimension instead of the original one. For numerical evaluation, we use our algorithm to build a recommender system and apply it to real-world datasets. The theoretical and numerical results demonstrate the effectiveness of our proposed algorithm compared to the state-of-the-art in terms of computational complexity and regret performance.