  We consider a distributed resource allocation problem in networks where each
transmitter-receiver pair aims at maximizing its local utility function by
adjusting its action matrix, which belongs to a given feasible set. This
problem has been addressed recently by applying a matrix exponential learning
(MXL) algorithm which has a very appealing convergence rate. In this learning
algorithm, however, each transmitter must know an estimate of the gradient
matrix of the local utility. The knowledge of the gradient matrix at the
transmitters incurs a high signaling overhead especially that the matrix size
increases with the dimension of the action matrix. In this paper, we therefore
investigate two strategies in order to decrease the informational exchange per
iteration of the algorithm. In the first strategy, each receiver sends at each
iteration part of the elements of the gradient matrix with respect to a certain
probability. In the second strategy, each receiver feeds back sporadically the
whole gradient matrix. We focus on the analysis of the convergence of the MXL
algorithm to optimum under these two strategies. We prove that the algorithm
can still converge to optimum almost surely. Upper bounds of the average
convergence rate are also derived in both situations with general step-size
setting, from which we can clearly see the impact of the incompleteness of the
feedback information. The proposed algorithms are applied to solve the energy
efficiency maximization problem in a multicarrier multi-user MIMO network.
Simulation results further corroborate our claim.
