A Primer on Online Convex Optimization

Abstract

We will start the presentation with the general Online Learning (OL) procedure. We will present one of the most important algorithms within the Online Cover Optimization (OCO) framework, the Online Mirror Descent (OMD), and we will give a brief intuitive connection to how OMD can adapt to different geometries of the feasible space in order to give solutions with performance guarantees. Then we will present Regret, one of the main metric considered in OCO, and the main OL benchmarks against which online algorithms are compared. We will see some results on the no-regret property (no-regret, i.e. asymptotic optimality, and negative results). We will also see some specific research works on which OCO has been applied as a solution and conclude by wrapping up with some use cases and discuss possible future directions where OCO could be a good tool and those where it is not an adequate tool, focusing on problems that arise within networking.