Adaptive randomized coordinate descent for solving sparse systems

Randomized coordinate descent (RCD), attractive for its robustness and ability to cope with large scale problems, is here investigated for the first time in an adaptive context. We present an RCD adaptive algorithm for finding sparse least-squares solutions to linear systems, in particular for FIR channel identification. The algorithm has low and tunable complexity and, as a special feature, adapts the probabilities with which the coordinates are chosen at each time moment. We show through simulation that the algorithm has tracking properties near those of the best current methods and investigate the trade-offs in the choices of the parameters.