Goal-oriented compression for $L_p$-norm-type goal functions: Application to power consumption scheduling

Abstract: Conventional data compression schemes aim at implementing a trade-off between the rate required to represent the compressed data and the resulting distortion between the original and reconstructed data. However, in more and more applications, what is desired is not reconstruction accuracy but the quality of the realization of a certain task by the receiver. In this paper, the receiver task is modeled by an optimization problem whose parameters have to be compressed by the transmitter. Motivated by applications such as the smart grid, this paper focuses on a goal function which is of $L_p$-norm-type. The aim is to design the precoding, quantization, and decoding stages such that the maximum of the goal function obtained with the compressed version of the parameters is as close as possible to the maximum obtained without compression. The numerical analysis, based on real smart grid signals, clearly shows the benefits of the proposed approach compared to the conventional distortion-based compression paradigm.