  Utilizing a human-perception-related objective function to train a speech
enhancement model has become a popular topic recently. The main reason is that
the conventional mean squared error (MSE) loss cannot represent auditory
perception well. One of the typical hu-man-perception-related metrics, which is
the perceptual evaluation of speech quality (PESQ), has been proven to provide
a high correlation to the quality scores rated by humans. Owing to its complex
and non-differentiable properties, however, the PESQ function may not be used
to optimize speech enhancement models directly. In this study, we propose
optimizing the enhancement model with an approximated PESQ function, which is
differentiable and learned from the training data. The experimental results
show that the learned surrogate function can guide the enhancement model to
further boost the PESQ score (in-crease of 0.18 points compared to the results
trained with MSE loss) and maintain the speech intelligibility.
