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

Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environments