CBRAP: Contextual Bandits with RAndom Projection.

Contextual bandits with linear payoffs, which are also known as linear bandits, provide a powerful alternative for solving practical problems of sequential decisions, e.g., online advertisements. In the era of big data, contextual data usually tend to be high-dimensional, which leads to new challenges for traditional linear bandits mostly designed for the setting of low-dimensional contextual data. Due to the curse of dimensionality, there are two challenges in most of the current bandit algorithms: the first is high time-complexity; and the second is extreme large upper regret bounds with high dimensional data. In this paper, in order to attack the above two challenges effectively, we develop an algorithm of Contextual Bandits via RAndom Projection (CBRAP) in the setting of linear payoffs, which works especially for high-dimensional contextual data. The proposed CBRAP algorithm is time-efficient and flexible, because it enables players to choose an arm in a low-dimensional space, and relaxes the sparsity assumption of constant number of non-zero components in previous work. Besides, we prove an upper regret bound for the proposed algorithm, which is associated with reduced dimensions. By comparing with three benchmark algorithms, we demonstrate improved performance on cumulative payoffs of CBRAP during its sequential decisions on both synthetic and real-world datasets, as well as its superior time-efficiency.