Cellular networks dynamically adjust the transmission parameters for a wireless link in response to its time-varying channel state. This is known as link adaptation, where the typical goal is to maximize the link throughput. State-of-the-art outer loop link adaptation (OLLA) selects the optimal transmission parameters based on an approximate, offline, model of the wireless link. Further, OLLA refines the offline model by dynamically compensating any deviations from the observed link performance. However, in practice, OLLA suffers from slow convergence and a sub-optimal link throughput. In this paper, we propose a link adaptation approach that overcomes the shortcomings of OLLA through a novel learning scheme. Our approach relies on contextual multi-armed bandits (MAB), where the context vector is composed of the instantaneous wireless channel state along with side information about the link. For a given context, our approach learns the success probability for each of the available transmission parameters, which is then exploited to select the throughput-maximizing parameters. Through numerical experiments, we show that our approach converges faster than OLLA and achieves a higher steady-state link throughput. For frequent and infrequent channel reports respectively, our scheme outperforms OLLA by 15% and 25% in terms of the steady-state link throughput. CCS CONCEPTS • Networks → Wireless access points, base stations and infrastructure; Network control algorithms; • Computing methodologies → Online learning settings.