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In this paper, we propose a novel algorithm for video bitrate adaptation in HTTP Adaptive Streaming (HAS), based on online learning. The proposed algorithm, named Learn2Adapt (L2A), is shown to provide a robust bitrate adaptation strategy which, unlike most of the state-of-the-art techniques, does not require parameter tuning, channel model assumptions, or application-specific adjustments. These properties make it very suitable for mobile users, who typically experience fast variations in channel characteristics. Experimental results, over real 4G traffic traces, show that L2A improves on the overall Quality of Experience (QoE) and in particular the average streaming bitrate, a result obtained independently of the channel and application scenarios.