  We propose a robust scheme for streaming 360-degree immersive videos to
maximize the quality of experience (QoE). Our streaming approach introduces a
holistic analytical framework built upon the formal method of stochastic
optimization. We propose a robust algorithm which provides a streaming rate
such that the video quality degrades below that rate with very low probability
even in presence of uncertain head movement, and bandwidth. It assumes the
knowledge of the viewing probability of different portions (tiles) of a
panoramic scene. Such probabilities can be easily derived from crowdsourced
measurements performed by 360 video content providers. We then propose
efficient methods to solve the problem at runtime while achieving a bounded
optimality gap (in terms of the QoE). We implemented our proposed approaches
using emulation. Using real users' head movement traces and real cellular
bandwidth traces, we show that our algorithms significantly outperform the
baseline algorithms by at least in $30\%$ in the QoE metric. Our algorithm
gives a streaming rate which is $50\%$ higher compared to the baseline
algorithms when the prediction error is high.
