  Edge Learning (EL) pushes the computational resources toward the edge of
5G/6G network to assist mobile users requesting delay-sensitive and
energy-aware intelligent services. A common challenge in running inference
tasks from remote is to extract and transmit only the features that are most
significant for the inference task. From this perspective, EL can be
effectively coupled with goal-oriented communications, whose aim is to transmit
only the information {\it relevant} to perform the inference task, under
prescribed accuracy, delay, and energy constraints. In this work, we consider a
multi-user/single server wireless network, where the users can
opportunistically decide whether to perform the inference task by themselves
or, alternatively, to offload the data to the edge server for remote
processing. The data to be transmitted undergoes a goal-oriented compression
stage performed using a convolutional encoder, jointly trained with a
convolutional decoder running at the edge-server side. Employing Lyapunov
optimization, we propose a method to jointly and dynamically optimize the
selection of the most suitable encoding/decoding scheme, together with the
allocation of computational and transmission resources, across all the users
and the edge server. Extensive simulations confirm the effectiveness of the
proposed approaches and highlight the trade-offs between energy, latency, and
learning accuracy.
