  The use of $\ell_p$ $(p=1,2)$ norms has largely dominated the measurement of
loss in neural networks due to their simplicity and analytical properties.
However, when used to assess the loss of visual information, these simple norms
are not very consistent with human perception. Here, we describe a different
"proximal" approach to optimize image analysis networks against quantitative
perceptual models. Specifically, we construct a proxy network, broadly termed
ProxIQA, which mimics the perceptual model while serving as a loss layer of the
network. We experimentally demonstrate how this optimization framework can be
applied to train an end-to-end optimized image compression network. By building
on top of an existing deep image compression model, we are able to demonstrate
a bitrate reduction of as much as $31\%$ over MSE optimization, given a
specified perceptual quality (VMAF) level.
