The unknotting number and reinforcement learning

May 22, 2023
The unknotting number of a knot K is the minimal number of crossing changes required to turn K into the unknot, taken over all diagrams of K. There is no algorithm known to compute it, and even finding the unknotting number of a fixed diagram becomes computationally unfeasible when the crossing number is large. Reinforcement learning is a machine learning paradigm where an agent learns to perform various actions by interacting with an environment in order to maximise a reward. I will discuss how reinforcement learning can help with the study of the unknotting number. This is joint work in progress with Sam Blackwell, Alex Davies, Thomas Edlich, and Marc Lackenby.