Gumbel-softmax-based optimization: a simple general framework for optimization problems on graphs

Computational Social Networks

Yueyuan Hou¹  Jing Liu²  Guozheng Lin²  Jiang Zhang²  Yaoxin Li²  Muyun Mou² 

[1] ColorfulClouds Tech, No. 04, Building C, 768 Creative Industrial Park, Compound 5A, Xueyuan Road, Haidian District, 100083, Beijing, People’s Republic of China;School of Systems Science, Beijing Normal University, No.19, Xinjiekouwai St, Haidian District, 100875, Beijing, People’s Republic of China;

关键词: Optimization problems on graphs;    Gumbel-softmax;    Evolution strategy;   

DOI  :  10.1186/s40649-021-00086-z

来源: Springer

【 摘 要 】

In computer science, there exist a large number of optimization problems defined on graphs, that is to find a best node state configuration or a network structure, such that the designed objective function is optimized under some constraints. However, these problems are notorious for their hardness to solve, because most of them are NP-hard or NP-complete. Although traditional general methods such as simulated annealing (SA), genetic algorithms (GA), and so forth have been devised to these hard problems, their accuracy and time consumption are not satisfying in practice. In this work, we proposed a simple, fast, and general algorithm framework based on advanced automatic differentiation technique empowered by deep learning frameworks. By introducing Gumbel-softmax technique, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We also introduce evolution strategy to parallel version of our algorithm. We test our algorithm on four representative optimization problems on graph including modularity optimization from network science, Sherrington–Kirkpatrick (SK) model from statistical physics, maximum independent set (MIS) and minimum vertex cover (MVC) problem from combinatorial optimization on graph, and Influence Maximization problem from computational social science. High-quality solutions can be obtained with much less time-consuming compared to the traditional approaches.

【 授权许可】

CC BY