Online Function Tracking with Generalized Penalties

We attend to the classic setting where an observer needs to inform a tracker about an arbitrary time varying function f : N0 → Z. This is an optimization problem, where both wrong values at the tracker and sending updates entail a certain cost. We consider an online variant of this problem, i.e., at time t, the observer only knows f(t′) for all t′ ≤ t. In this paper, we generalize existing cost models (with an emphasis on concave and convex penalties) and present two online algorithms. Our analysis shows that these algorithms perform well in a large class of models, and are even optimal in some settings.