This paper provides a quantitative notion of the sparsity for infinite dimensional atomic spaces, which play an important role in many signal processing applications. This notion of sparsity is defined as the ratio of the number of redundant samples (not necessary to recover any signal in the atomic space) to the number of all available samples of a particular canonical sampling system. It is shown that the so defined sparsity can be expressed in terms of the support of the spectral density of the sequence which generates the atomic space.
We consider a class of concave continuous games in which the corresponding admissible strategy profile of each player underlies affine coupling constraints. We propose a novel algorithm that leads the corresponding population dynamic toward Nash equilibrium. This algorithm is based on a mirror ascent algorithm, which suits with the framework of no-regret online learning, and on the augmented Lagrangian method. The decentralization aspect of the algorithm corresponds to the aspects that the iterate of each player requires the local information of about how she contributes to the coupling constraints and the price vector broadcasted by a central coordinator. So each player need not know about the population action. Moreover, no specific control by the central coordinator is required. We give a condition on the step sizes and the degree of the augmentation of the Lagrangian, such that the proposed algorithm converges to a generalized Nash equilibrium.
Competitive non-cooperative online decision-making agents whose actions increase congestion of scarce resources constitute a model for widespread modern large-scale applications. To ensure sustainable resource behavior, we introduce a novel method to steer the agents toward a stable population state, fulfilling the given coupled resource constraints. The proposed method is a decentralized resource pricing method based on the resource loads resulting from the augmentation of the game's Lagrangian. Assuming that the online learning agents have only noisy first-order utility feedback, we show that for a polynomially decaying agents' step size/learning rate, the population's dynamic will almost surely converge to generalized Nash equilibrium. A particular consequence of the latter is the fulfillment of resource constraints in the asymptotic limit. Moreover, we investigate the finite-time quality of the proposed algorithm by giving a nonasymptotic time decaying bound for the expected amount of resource constraint violation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.