More Adaptive Algorithms for Tracking the Best Expert
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In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and derive novel data-dependent bounds by developing two adaptive algorithms. The first algorithm achieves a second-order tracking regret bound, which improves existing first-order bounds. The second algorithm enjoys a path-length bound, which is generally incomparable to the second-order bound but offers advantages in slowly moving environments. Both algorithms are developed under the online mirror descent framework and draw inspiration from existing algorithms that attain data-dependent bounds of static regret. The key idea is to use a clipped simplex in the updating step of online mirror descent. Finally, we extend our algorithms and analysis to the problem of online matrix prediction and provide the first data-dependent tracking regret bound for this problem.
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