A Stochastic Majorize-Minimize Subspace Algorithm for Online Penalized Least Squares Estimation

Stochastic approximation techniques play an important role in solving many encountered in machine learning or adaptive signal processing. In contexts, the statistics of the data are often unknown a priori or their computation is too intensive, and they have thus to be estimated online the observed signals. For batch optimization of an objective function the sum of a data fidelity term and a penalization (e.g. a sparsity function), Majorize-Minimize (MM) methods have recently attracted interest since they are fast, highly flexible, and effective in ensuring. The goal of this paper is to show how these methods can be extended to the case when the data fidelity term corresponds to a squares criterion and the cost function is replaced by a sequence of approximations of it. In this context, we propose an online version an MM subspace algorithm and we study its convergence by using suitable tools. Simulation results illustrate the good practical of the proposed algorithm associated with a memory gradient, when applied to both non-adaptive and adaptive filter identification.