  Applications involving dictionary learning, non-negative matrix
factorization, subspace clustering, and parallel factor tensor decomposition
tasks motivate well algorithms for per-block-convex and non-smooth optimization
problems. By leveraging the stochastic approximation paradigm and first-order
acceleration schemes, this paper develops an online and modular learning
algorithm for a large class of non-convex data models, where convexity is
manifested only per-block of variables whenever the rest of them are held
fixed. The advocated algorithm incurs computational complexity that scales
linearly with the number of unknowns. Under minimal assumptions on the cost
functions of the composite optimization task, without bounding constraints on
the optimization variables, or any explicit information on bounds of Lipschitz
coefficients, the expected cost evaluated online at the resultant iterates is
provably convergent with quadratic rate to an accumulation point of the
(per-block) minima, while subgradients of the expected cost asymptotically
vanish in the mean-squared sense. The merits of the general approach are
demonstrated in two online learning setups: (i) Robust linear regression using
a sparsity-cognizant total least-squares criterion; and (ii) semi-supervised
dictionary learning for network-wide link load tracking and imputation with
missing entries. Numerical tests on synthetic and real data highlight the
potential of the proposed framework for streaming data analytics by
demonstrating superior performance over block coordinate descent, and reduced
complexity relative to the popular alternating-direction method of multipliers.
