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

Abstract

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.

Deep Stochastic Logic Gate Networks

“…The Gumbel Softmax is widely used for gradient-based optimization in differentiable neural networks. Additionally, it has applications in solving combinatorial problems and addressing inverse problems with discrete multivariate random variables [41], [42].…”

Inferring cancer type-specific patterns of metastatic spread

“…In order to capture multiple modes of the posterior distribution, we optimize multiple Vs in parallel. To do this, we set up steps 1-3 such that x Âs are solved for in parallel 51 , where x is equal to the sample size and is calculated according to the size of the inputs (Ã K C ). See Supplementary Information for further explanation.…”