  We propose an alternating minimization heuristic for regression over the
space of tropical rational functions with fixed exponents. The method
alternates between fitting the numerator and denominator terms via tropical
polynomial regression, which is known to admit a closed form solution. We
demonstrate the behavior of the alternating minimization method experimentally.
Experiments demonstrate that the heuristic provides a reasonable approximation
of the input data. Our work is motivated by applications to ReLU neural
networks, a popular class of network architectures in the machine learning
community which are closely related to tropical rational functions.
