The paper proves the first second-order tracking regret bound for prediction with expert advice, an efficient path-length bound, and the first data-dependent tracking regret bound for online matrix prediction.
A closer look at adaptive regret
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Adaptive and Efficient Algorithms for Tracking the Best Expert
The paper proves the first second-order tracking regret bound for prediction with expert advice, an efficient path-length bound, and the first data-dependent tracking regret bound for online matrix prediction.