46 research outputs found
Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms with Directed Gossip Communication
We study distributed optimization in networked systems, where nodes cooperate
to find the optimal quantity of common interest, x=x^\star. The objective
function of the corresponding optimization problem is the sum of private (known
only by a node,) convex, nodes' objectives and each node imposes a private
convex constraint on the allowed values of x. We solve this problem for generic
connected network topologies with asymmetric random link failures with a novel
distributed, decentralized algorithm. We refer to this algorithm as AL-G
(augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented
Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast
gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual
function. Dual variables are updated by the standard method of multipliers, at
a slow time scale. To update the primal variables, we propose a novel,
Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses
unidirectional gossip communication, only between immediate neighbors in the
network and is resilient to random link failures. For networks with reliable
communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian
broadcast gossiping) algorithm reduces communication, computation and data
storage cost. We prove convergence for all proposed algorithms and demonstrate
by simulations the effectiveness on two applications: l_1-regularized logistic
regression for classification and cooperative spectrum sensing for cognitive
radio networks.Comment: 28 pages, journal; revise
Slotted Aloha for Networked Base Stations
We study multiple base station, multi-access systems in which the user-base
station adjacency is induced by geographical proximity. At each slot, each user
transmits (is active) with a certain probability, independently of other users,
and is heard by all base stations within the distance . Both the users and
base stations are placed uniformly at random over the (unit) area. We first
consider a non-cooperative decoding where base stations work in isolation, but
a user is decoded as soon as one of its nearby base stations reads a clean
signal from it. We find the decoding probability and quantify the gains
introduced by multiple base stations. Specifically, the peak throughput
increases linearly with the number of base stations and is roughly
larger than the throughput of a single-base station that uses standard slotted
Aloha. Next, we propose a cooperative decoding, where the mutually close base
stations inform each other whenever they decode a user inside their coverage
overlap. At each base station, the messages received from the nearby stations
help resolve collisions by the interference cancellation mechanism. Building
from our exact formulas for the non-cooperative case, we provide a heuristic
formula for the cooperative decoding probability that reflects well the actual
performance. Finally, we demonstrate by simulation significant gains of
cooperation with respect to the non-cooperative decoding.Comment: conference; submitted on Dec 15, 201