In recent years, HTTP Adaptive Streaming (HAS) is becoming the de-facto standard for adaptive video streaming services. A HAS video consists of multiple segments, encoded at multiple quality levels. State-of-the-art HAS clients employ deterministic heuristics to dynamically adapt the requested quality level based on the perceived network conditions. Current HAS client heuristics are however hardwired to fit specific network configurations, making them less flexible to fit a vast range of settings. In this article, a (Frequency Adjusted)Q-Learning HAS client is proposed. In contrast to existing heuristics, the proposed HAS client dynamically learns the optimal behaviour corresponding to the current network environment in order to optimize the Quality of Experience (QoE). Furthermore, the client has been optimized both in terms of global performance and convergence speed. Thorough evaluations show that the proposed client can outperform deterministic algorithms by 11% to 18% in terms of Mean Opinion Score (MOS) in a wide range of network configurations.