  Edge machine learning can deliver low-latency and private artificial
intelligent (AI) services for mobile devices by leveraging computation and
storage resources at the network edge. This paper presents an energy-efficient
edge processing framework to execute deep learning inference tasks at the edge
computing nodes whose wireless connections to mobile devices are prone to
channel uncertainties. Aimed at minimizing the sum of computation and
transmission power consumption with probabilistic quality-of-service (QoS)
constraints, we formulate a joint inference tasking and downlink beamforming
problem that is characterized by a group sparse objective function. We provide
a statistical learning based robust optimization approach to approximate the
highly intractable probabilistic-QoS constraints by nonconvex quadratic
constraints, which are further reformulated as matrix inequalities with a
rank-one constraint via matrix lifting. We design a reweighted power
minimization approach by iteratively reweighted $\ell_1$ minimization with
difference-of-convex-functions (DC) regularization and updating weights, where
the reweighted approach is adopted for enhancing group sparsity whereas the DC
regularization is designed for inducing rank-one solutions. Numerical results
demonstrate that the proposed approach outperforms other state-of-the-art
approaches.
