5 research outputs found
A Sparsity-Aware Adaptive Algorithm for Distributed Learning
In this paper, a sparsity-aware adaptive algorithm for distributed learning
in diffusion networks is developed. The algorithm follows the set-theoretic
estimation rationale. At each time instance and at each node of the network, a
closed convex set, known as property set, is constructed based on the received
measurements; this defines the region in which the solution is searched for. In
this paper, the property sets take the form of hyperslabs. The goal is to find
a point that belongs to the intersection of these hyperslabs. To this end,
sparsity encouraging variable metric projections onto the hyperslabs have been
adopted. Moreover, sparsity is also imposed by employing variable metric
projections onto weighted balls. A combine adapt cooperation strategy
is adopted. Under some mild assumptions, the scheme enjoys monotonicity,
asymptotic optimality and strong convergence to a point that lies in the
consensus subspace. Finally, numerical examples verify the validity of the
proposed scheme, compared to other algorithms, which have been developed in the
context of sparse adaptive learning
Quasinonexpansive Iterations on the Affine Hull of Orbits: From Mann's Mean Value Algorithm to Inertial Methods
Fixed point iterations play a central role in the design and the analysis of
a large number of optimization algorithms. We study a new iterative scheme in
which the update is obtained by applying a composition of quasinonexpansive
operators to a point in the affine hull of the orbit generated up to the
current iterate. This investigation unifies several algorithmic constructs,
including Mann's mean value method, inertial methods, and multi-layer
memoryless methods. It also provides a framework for the development of new
algorithms, such as those we propose for solving monotone inclusion and
minimization problems