Reinforcement learning (RL) is a subfield of machine learning that focuses on developing models that can autonomously learn optimal decision-making strategies over time. In a recent pioneering paper, Wagner demonstrated how the Deep Cross-Entropy RL method can be applied to tackle various problems from extremal graph theory by reformulating them as combinatorial optimization problems. Subsequently, many researchers became interested in refining and extending the framework introduced by Wagner, thereby creating various RL environments specialized for graph theory. Moreover, a number of problems from extremal graph theory were solved through the use of RL. In particular, several inequalities concerning the Laplacian spectral radius of graphs were refuted, new lower bounds were obtained for certain Ramsey numbers, and contributions were made to the Turán-type extremal problem in which the forbidden structures are cycles of length three and four. Here, we present Reinforcement Learning for Graph Theory (RLGT), a novel RL framework that systematizes the previous work and provides support for both undirected and directed graphs, with or without loops, and with an arbitrary number of edge colors. The framework efficiently represents graphs and aims to facilitate future RL-based research in extremal graph theory through optimized computational performance and a clean and modular design.

翻译：强化学习（Reinforcement Learning，RL）是机器学习的一个子领域，专注于开发能够随时间自主习得最优决策策略的模型。在近期一篇开创性论文中，Wagner 展示了如何通过将极值图论中的各类问题重新表述为组合优化问题，并应用深度交叉熵强化学习方法加以求解。此后，众多研究者对改进和拓展 Wagner 提出的框架产生浓厚兴趣，由此开发出多种专门面向图论问题的强化学习环境。此外，已有若干极值图论问题借助强化学习得以解决。具体而言，研究否定了若干关于图谱拉普拉斯半径的不等式，获得了某些拉姆齐数的新下界，并对禁止结构为三阶与四阶环的图兰型极值问题作出了贡献。本文提出 RLGT（Reinforcement Learning for Graph Theory），这是一个新颖的强化学习框架，它系统整合了先前工作，支持无向图与有向图（允许或不允许自环），并可处理任意数量的边着色。该框架实现了高效的图结构表示，并通过优化的计算性能与清晰模块化的设计，旨在为未来基于强化学习的极值图论研究提供支持。