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

TL;DR

This paper introduces a goal-oriented compression method tailored for $L_p$-norm-type functions, optimizing data encoding for specific task performance rather than traditional accuracy, demonstrated through smart grid applications.

Contribution

It proposes a novel compression framework focusing on goal functions, especially $L_p$-norms, with practical algorithms and validation on real smart grid data.

Findings

Improved goal function preservation compared to traditional methods

Effective compression for smart grid parameter optimization

Numerical results show significant performance gains

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.