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 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.
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