# Reinforcement learning for graph theory, Parallelizing Wagner's approach

arXiv: https://arxiv.org/abs/2509.01607 · HTML: https://mlsanity.com/paper/2509.01607/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 8 of its 19 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Population Based Training of Neural Networks](https://mlsanity.com/paper/1711.09846/) (2017)
- [Constructions in combinatorics via neural networks](https://mlsanity.com/paper/2104.14516/) (2021)
- [Action Space Shaping in Deep Reinforcement Learning](https://mlsanity.com/paper/2004.00980/) (2020)
- [PatternBoost: Constructions in Mathematics with a Little Help from AI](https://mlsanity.com/paper/2411.00566/) (2024)
- [A Simple Decentralized Cross-Entropy Method](https://mlsanity.com/paper/2212.08235/) (2022)
- [Tempestas ex machina: A review of machine learning methods for wavefront control](https://mlsanity.com/paper/2309.00730/) (2023)

## Abstract (arXiv)

Our work applies reinforcement learning to construct counterexamples concerning conjectured bounds on the spectral radius of the Laplacian matrix of a graph. We expand upon the re-implementation of Wagner's approach by Stevanovic et al. with the ability to train numerous unique models simultaneously and a novel redefining of the action space to adjust the influence of the current local optimum on the learning process.