Abstract by Jamison Moody
Reinforcement Learning in Knot Theory
One fundamental question in knot theory involves determining whether two given knot diagrams represent the same knot. One potential way to address this problem is through reinforcement learning (RL), which involves training algorithms to learn to make decisions by giving them positive or negative feedback (rewards). By using two relatively new algorithms in RL, called Augmented Random Search and Evolution Strategies, I investigate whether it is possible to reduce complicated knots diagrams to simpler forms, by minimizing the number of crossings. By solving this problem of knot simplification, we can more easily tell if two knot diagrams represent the same knot. I design models that use the Gauss-code manipulation program Jonathan Edevold and I created. I will discuss some preliminary results and describe how the algorithms behave before and after training.