Distributed learning for resource allocation under uncertainty

In this paper, we present a distributed matrix exponential learning (MXL) algorithm for a wide range of distributed optimization problems and games that arise in signal processing and data networks. To analyze it, we introduce a novel stability concept that guarantees the existence of a unique equilibrium solution; under this condition, we show that the algorithm converges even in the presence of highly defective feedback that is subject to measurement noise, errors, etc. For illustration purposes, we apply the proposed method to the problem of energy efficiency (EE) maximization in multi-user, multiple-antenna wireless networks with imperfect channel state information (CSI), showing that users quickly achieve a per capita EE gain between 100% and 400%, even under very high uncertainty.