Online convex optimization meets sparsity

Tracking time-varying sparse signals is a recent problem with widespread applications. Techniques derived from compressed sensing, Lasso, and Kalman filtering have been proposed in the literature, which mainly present two drawbacks: the prior knowledge of specific evolution models and the lack of theoretical guarantees. In this work, we propose a new perspective on the problem, based on the theory on online convex optimization, which has been developed in the machine learning community. We exploit a strongly convex model, and we develop online algorithms, for which we are able to provide a dynamic regret analysis. A few simulations that support the theoretical results are finally presented.