Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search

Abbas Mehrabian, Ankit Anand, Hyunjik Kim, Nicolas Sonnerat, Tudor Berariu, Matej Balog, Gheorghe Comanici, Andrew Lee, Anian Ruoss, Anna Bulanova, Daniel Toyama, Sam Blackwell, Bernardino Romera Paredes, Laurent Orseau, Petar Veličković, Anurag Murty Naredla, Joonkyung Lee, Adam Zsolt Wagner, Doina Precup

Keywords: AlphaZero, tabu search, graph theory, curriculum

TL;DR: Solving extremal graph problems using AlphaZero and tabu search with curriculum

Abstract: This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdős, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum---jump-starting the search for larger graphs using good graphs found at smaller sizes---we improve the state-of-the-art lower bounds for several sizes. Lastly, we propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

Submission Number: 21