  Register allocation is one of the most important problems for modern
compilers. With a practically unlimited number of user variables and a small
number of CPU registers, assigning variables to registers without conflicts is
a complex task. This work demonstrates the use of casting the register
allocation problem as a graph coloring problem. Using technologies such as
PyTorch and OpenAI Gymnasium Environments we will show that a Proximal Policy
Optimization model can learn to solve the graph coloring problem. We will also
show that the labeling of a graph is critical to the performance of the model
by taking the matrix representation of a graph and permuting it. We then test
the model's effectiveness on each of these permutations and show that it is not
effective when given a relabeling of the same graph. Our main contribution lies
in showing the need for label reordering invariant representations of graphs
for machine learning models to achieve consistent performance.
