Optimizing Pseudo-Boolean Polynomials using Hypergraph Neural Networks

Andrei Ermakov, Ilya Makarov

Keywords: HGNN, Combinatorial Optimization, PUBO, Pseudo-Boolean Polynomials

TL;DR: We introduce PB-HGNN, the first unsupervised hypergraph neural network framework that directly optimizes high-order pseudo-Boolean polynomials

Abstract: The challenge of solving NP-hard combinatorial optimization problems with deep learning has attracted considerable interest. Modern graph neural networks are capable of efficiently solving problem instances in an unsupervised manner, however the graph structure limits the scope of their application. We present a novel approach, hereafter referred to as PB-HGNN, which employs unsupervised Hypergraph Neural Networks (HGNNs) to solve the polynomial unconstrained binary optimization (PUBO) problem. By representing the high-order terms of the pseudo-Boolean polynomials as hyperedges in a hypergraph, the HGNN is enable to capture intricate variable interdependencies beyond pairwise interactions. As a result, our framework provides the possibility of solving a wide range of discrete problems that have not previously been addressed by neural networks. We evaluate PB-HGNN on random higher-order pseudo-Boolean polynomials, including the Sherrington-Kirkpatrick model, and max-3-SAT instances. Our results show that PB-HGNN outperforms baselines on these problems and is capable of solving large-scale PUBO instances.

Primary Area: optimization

Submission Number: 5299