The CEO Problem with rth Power of Difference Distortion

The CEO problem has received a lot of attention since Berger et al. first investigated it, however, there are limited results on non-Gaussian models with non-quadratic distortion measures. In this work, we extend the CEO problem to two continuous-alphabet settings with general rth power of difference distortion, and study asymptotics of distortion as the number of agents and sum rate grow without bound. The first setting is a regular source-observation model, such as jointly Gaussian, with difference distortion and we show that the distortion decays at $R_{{\text{sum}}}^{ - r/2}$ up to a multiplicative constant. The other setting is a non-regular source-observation model, such as copula or uniform additive noise models, for which estimation-theoretic regularity conditions do not hold. The optimal decay R−rsum is obtained for the non-regular model.