This work examines the performance of stochastic sub-gradient learning strategies, for both cases of stand-alone and networked agents, under weaker conditions than usually considered in the literature. It is shown that these conditions are automatically satisfied by several important cases of interest, including support-vector machines and sparsity-inducing learning solutions. The analysis establishes that sub-gradient strategies can attain exponential convergence rates, as opposed to sub-linear rates, and that they can approach the optimal solution within O(p), for sufficiently small step-sizes, p. A realizable exponential-weighting procedure is proposed to smooth the intermediate iterates and to guarantee these desirable performance properties.