Goal-Oriented 1-bit Quantization With Uncertain Distortion Measures

Tailoring low resolution quantization to specific tasks is an important aspect of goal-oriented communications, with applications ranging from feedback for multiple-input multiple-output (MIMO) systems to compression of neural network weights. However, target distortion functions associated with a task may either be imperfectly known or intractable to compute, leading to uncertainty in the distortion function. In this letter, we propose new criteria based on risk measures to design 1-bit quantizers with uncertainty in the distortion function. While information-theoretic limits of compression with risk measure constraints have recently been established, quantizers based on risk measure criteria have not yet been developed. We introduce an algorithm for quantizer design with our risk measure criteria based on the cross-entropy method, and apply our approach to an environmental monitoring dataset.