Adaptive and Efficient Algorithms for Tracking the Best Expert
This work addresses the challenge of tracking the best expert in dynamic prediction settings, representing an incremental improvement over existing methods.
The paper tackles the problem of prediction with expert advice in dynamic environments by developing two adaptive algorithms with data-dependent tracking regret bounds: one achieves a second-order bound that improves existing first-order bounds, and the other offers a path-length bound advantageous in slowly moving environments, with both extended to online matrix prediction to provide the first data-dependent tracking regret bound for that problem.
In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and develop two adaptive and efficient algorithms with data-dependent tracking regret bounds. 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 not comparable 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 online matrix prediction and provide the first data-dependent tracking regret bound for this problem.