  Decentralized optimization strategies are helpful for various applications,
from networked estimation to distributed machine learning. This paper studies
finite-sum minimization problems described over a network of nodes and proposes
a computationally efficient algorithm that solves distributed convex problems
and optimally finds the solution to locally non-convex objective functions. In
contrast to batch gradient optimization in some literature, our algorithm is on
a single-time scale with no extra inner consensus loop. It evaluates one
gradient entry per node per time. Further, the algorithm addresses link-level
nonlinearity representing, for example, logarithmic quantization of the
exchanged data or clipping of the exchanged data bits. Leveraging
perturbation-based theory and algebraic Laplacian network analysis proves
optimal convergence and dynamics stability over time-varying and switching
networks. The time-varying network setup might be due to packet drops or link
failures. Despite the nonlinear nature of the dynamics, we prove exact
convergence in the face of odd sign-preserving sector-bound nonlinear data
transmission over the links. Illustrative numerical simulations further
highlight our contributions.
