Centralized and distributed online learning for sparse time-varying optimization
This work addresses the need for model-free and adversarial approaches in sparse time-varying optimization, which is incremental as it builds on existing online convex optimization frameworks.
The paper tackled the problem of tracking time-varying systems without prior knowledge of their evolution, proposing centralized and distributed online learning algorithms for sparse time-varying optimization, and demonstrated their effectiveness through theoretical analysis and numerical experiments.
The development of online algorithms to track time-varying systems has drawn a lot of attention in the last years, in particular in the framework of online convex optimization. Meanwhile, sparse time-varying optimization has emerged as a powerful tool to deal with widespread applications, ranging from dynamic compressed sensing to parsimonious system identification. In most of the literature on sparse time-varying problems, some prior information on the system's evolution is assumed to be available. In contrast, in this paper, we propose an online learning approach, which does not employ a given model and is suitable for adversarial frameworks. Specifically, we develop centralized and distributed algorithms, and we theoretically analyze them in terms of dynamic regret, in an online learning perspective. Further, we propose numerical experiments that illustrate their practical effectiveness.