  This work examines the mean-square error performance of diffusion stochastic
algorithms under a generalized coordinate-descent scheme. In this setting, the
adaptation step by each agent is limited to a random subset of the coordinates
of its stochastic gradient vector. The selection of coordinates varies randomly
from iteration to iteration and from agent to agent across the network. Such
schemes are useful in reducing computational complexity at each iteration in
power-intensive large data applications. They are also useful in modeling
situations where some partial gradient information may be missing at random.
Interestingly, the results show that the steady-state performance of the
learning strategy is not always degraded, while the convergence rate suffers
some degradation. The results provide yet another indication of the resilience
and robustness of adaptive distributed strategies.
