  In the past few years, Online Convex Optimization (OCO) has received notable
attention in the control literature thanks to its flexible real-time nature and
powerful performance guarantees. In this paper, we propose new step-size rules
and OCO algorithms that simultaneously exploit gradient predictions, function
predictions and dynamics, features particularly pertinent to control
applications. The proposed algorithms enjoy static and dynamic regret bounds in
terms of the dynamics of the reference action sequence, gradient prediction
error, and function prediction error, which are generalizations of known
regularity measures from the literature. We present results for both convex and
strongly convex costs. We validate the performance of the proposed algorithms
in a trajectory tracking case study, as well as portfolio optimization using
real-world datasets.
