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arXiv · 2410.01661

Finding path and cycle counting formulae in graphs with Deep Reinforcement Learning

Jason Piquenot·Maxime Bérar·Pierre Héroux·Jean-Yves Ramel·Romain Raveaux·Sébastien Adam
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Abstract

This paper presents Grammar Reinforcement Learning (GRL), a reinforcement learning algorithm that uses Monte Carlo Tree Search (MCTS) and a transformer architecture that models a Pushdown Automaton (PDA) within a context-free grammar (CFG) framework. Taking as use case the problem of efficiently counting paths and cycles in graphs, a key challenge in network analysis, computer science, biology, and social sciences, GRL discovers new matrix-based formulas for path/cycle counting that improve computational efficiency by factors of two to six w.r.t state-of-the-art approaches. Our contributions include: (i) a framework for generating gramformers that operate within a CFG, (ii) the development of GRL for optimizing formulas within grammatical structures, and (iii) the discovery of novel formulas for graph substructure counting, leading to significant computational improvements.

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Jason Piquenot, Maxime Bérar, Pierre Héroux, Jean-Yves Ramel, Romain Raveaux, Sébastien Adam. 2024-10-02. Finding path and cycle counting formulae in graphs with Deep Reinforcement Learning. https://arxiv.org/abs/2410.01661

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