  Stochastic optimization algorithms update models with cheap per-iteration
costs sequentially, which makes them amenable for large-scale data analysis.
Such algorithms have been widely studied for structured sparse models where the
sparsity information is very specific, e.g., convex sparsity-inducing norms or
$\ell^0$-norm. However, these norms cannot be directly applied to the problem
of complex (non-convex) graph-structured sparsity models, which have important
application in disease outbreak and social networks, etc. In this paper, we
propose a stochastic gradient-based method for solving graph-structured
sparsity constraint problems, not restricted to the least square loss. We prove
that our algorithm enjoys a linear convergence up to a constant error, which is
competitive with the counterparts in the batch learning setting. We conduct
extensive experiments to show the efficiency and effectiveness of the proposed
algorithms.
