  Collaborative Edge Computing (CEC) is an emerging paradigm that collaborates
heterogeneous edge devices as a resource pool to compute DNN inference tasks in
proximity such as edge video analytics. Nevertheless, as the key knob to
improve network utility in CEC, existing works mainly focus on the workload
routing strategies among edge devices with the aim of minimizing the routing
cost, remaining an open question for joint workload allocation and routing
optimization problem from a system perspective. To this end, this paper
presents a holistic, learned optimization for CEC towards maximizing the total
network utility in an online manner, even though the utility functions of task
input rates are unknown a priori. In particular, we characterize the CEC system
in a flow model and formulate an online learning problem in a form of
cross-layer optimization. We propose a nested-loop algorithm to solve workload
allocation and distributed routing iteratively, using the tools of gradient
sampling and online mirror descent. To improve the convergence rate over the
nested-loop version, we further devise a single-loop algorithm. Rigorous
analysis is provided to show its inherent convexity, efficient convergence, as
well as algorithmic optimality. Finally, extensive numerical simulations
demonstrate the superior performance of our solutions.
