1 research outputs found
Completely Uncoupled Algorithms for Network Utility Maximization
In this paper, we present two completely uncoupled algorithms for utility
maximization. In the first part, we present an algorithm that can be applied
for general non-concave utilities. We show that this algorithm induces a
perturbed (by ) Markov chain, whose stochastically stable states are
the set of actions that maximize the sum utility. In the second part, we
present an approximate sub-gradient algorithm for concave utilities which is
considerably faster and requires lesser memory. We study the performance of the
sub-gradient algorithm for decreasing and fixed step sizes. We show that, for
decreasing step sizes, the Cesaro averages of the utilities converges to a
neighbourhood of the optimal sum utility. For constant step size, we show that
the time average utility converges to a neighbourhood of the optimal sum
utility. Our main contribution is the expansion of the achievable rate region,
which has been not considered in the prior literature on completely uncoupled
algorithms for utility maximization. This expansion aids in allocating a fair
share of resources to the nodes which is important in applications like channel
selection, user association and power control