James B. Robinson

James Robinson, Mark Herbster

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.

Mark Herbster, James Robinson

We address the problem of predicting the labeling of a graph in an online setting when the labeling is changing over time. We present an algorithm based on a specialist approach; we develop the machinery of cluster specialists which probabilistically exploits the cluster structure in the graph. Our algorithm has two variants, one of which surprisingly only requires $\mathcal{O}(\log n)$ time on any trial $t$ on an $n$-vertex graph, an exponential speed up over existing methods. We prove switching mistake-bound guarantees for both variants of our algorithm. Furthermore these mistake bounds smoothly vary with the magnitude of the change between successive labelings. We perform experiments on Chicago Divvy Bicycle Sharing data and show that our algorithms significantly outperform an existing algorithm (a kernelized Perceptron) as well as several natural benchmarks.