Finding Counterexamples to Conjectures via Reinforcement Learning - IPAM at UCLA

Explore a groundbreaking approach to solving mathematical conjectures in this 50-minute lecture by Adam Wagner from Worcester Polytechnic Institute. Dive into the application of reinforcement learning, specifically the cross-entropy method, to find counterexamples in graph theory and combinatorics. Discover how a simple setup with minimal modifications can tackle a wide range of problems, leading to the resolution of open questions and the discovery of more elegant counterexamples to previously disproved conjectures. Learn about the practical implementation of this method, including reward functions, RL setups, and potential challenges. Gain insights into solving infinite problems, addressing non-obvious reward functions, and improving the overall approach. Recorded at IPAM's Machine Assisted Proofs Workshop at UCLA, this talk offers a fascinating glimpse into the intersection of machine learning and mathematical problem-solving.

Intro
Talk overview
Reinforcement learning
Example 1
What if we don't succeed?
Example 2
Not just graphs
Example 3
Example 4 - Problems on trees
non-obvious reward function
Example 5
Example 6 - Infinite problems?
What RL setup to use?
Reasons an RL algorithm might not work
Practical problems
Cross-entropy method
Implementation details
Improvements to the method