In designing an HTTP adaptive streaming (HAS) system, the bitrate adaptation scheme in the player is a key component to ensure a good quality of experience (QoE) for viewers. We propose a new online reinforcement learning optimization framework, called ORL-SDN, targeting HAS players running in a software-defined networking (SDN) environment. We leverage SDN to facilitate the orchestration of the adaptation schemes for a set of HAS players. To reach a good level of QoE fairness in a large population of players, we cluster them based on a perceptual quality index. We formulate the adaptation process as a Partially Observable Markov Decision Process and solve the per-cluster optimization problem using an online Q-learning technique that leverages model predictive control and parallelism via aggregation to avoid a per-cluster suboptimal selection and to accelerate the convergence to an optimum. This framework achieves maximum long-term revenue by selecting the optimal representation for each cluster under time-varying network conditions. The results show that ORL-SDN delivers substantial improvements in viewer QoE, presentation quality stability, fairness, and bandwidth utilization over well-known adaptation schemes.