Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environments

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 article, 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.