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In this paper, we propose a novel algorithm for video quality adaptation in HTTP Adaptive Streaming (HAS), based on Online Convex Optimization (OCO). The proposed algorithm, named Learn2Adapt (L2A), is shown to provide a robust adaptation strategy which, unlike most of the state-ofthe-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. Simulations show that L2A improves on average streaming bit-rate without impairing the overall Quality of Experience (QoE), a result that is independent of the channel and application scenarios.