Improved Regret Bounds for Tracking Experts with Memory
This work addresses a theoretical challenge in online learning for non-stationary settings, offering incremental improvements in regret bounds.
The paper tackles the problem of sequential prediction with expert advice in non-stationary environments with long-term memory guarantees, resulting in a linear-time algorithm that improves on the best known regret bounds.
We address the problem of sequential prediction with expert advice in a non-stationary environment with long-term memory guarantees in the sense of Bousquet and Warmuth [4]. We give a linear-time algorithm that improves on the best known regret bounds [26]. This algorithm incorporates a relative entropy projection step. This projection is advantageous over previous weight-sharing approaches in that weight updates may come with implicit costs as in for example portfolio optimization. We give an algorithm to compute this projection step in linear time, which may be of independent interest.