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 pro- cessing 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, er- rors, etc. For illustration purposes, we apply the proposed method to the problem of energy efficiency (EE) maximiza- tion 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.