  With the rapid upsurge of deep learning tasks at the network edge, effective
edge artificial intelligence (AI) inference becomes critical to provide
low-latency intelligent services for mobile users via leveraging the edge
computing capability. In such scenarios, energy efficiency becomes a primary
concern. In this paper, we present a joint inference task selection and
downlink beamforming strategy to achieve energy-efficient edge AI inference
through minimizing the overall power consumption consisting of both computation
and transmission power consumption, yielding a mixed combinatorial optimization
problem. By exploiting the inherent connections between the set of task
selection and group sparsity structural transmit beamforming vector, we
reformulate the optimization as a group sparse beamforming problem. To solve
this challenging problem, we propose a log-sum function based three-stage
approach. By adopting the log-sum function to enhance the group sparsity, a
proximal iteratively reweighted algorithm is developed. Furthermore, we
establish the global convergence analysis and provide the ergodic worst-case
convergence rate for this algorithm. Simulation results will demonstrate the
effectiveness of the proposed approach for improving energy efficiency in edge
AI inference systems.
