Reinforcement Learning for Graph Coloring: Understanding the Power and Limits of Non-Label Invariant Representations

• URL: http://arxiv.org/abs/2401.12470v1
• Date: Tue, 23 Jan 2024 03:43:34 GMT
• Title: Reinforcement Learning for Graph Coloring: Understanding the Power and Limits of Non-Label Invariant Representations
• Authors: Chase Cummins and Richard Veras
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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