UniHetCO: A Unified Heterogeneous Representation for Multi-Problem Learning in Unsupervised Neural Combinatorial Optimization

2026-03-11

AI Summary

This work proposes UniHetCO, a unified unsupervised framework for jointly learning multiple classes of constrained quadratic combinatorial optimization problems, addressing the limited generalizability of existing unsupervised neural methods that typically target individual tasks. UniHetCO constructs a heterogeneous graph representation to jointly encode problem structure, objective functions, and linear constraints. To enhance training stability, it introduces a gradient-norm-based dynamic loss weighting mechanism. Experimental results demonstrate that UniHetCO achieves performance comparable to state-of-the-art unsupervised methods across four distinct node subset selection tasks—including maximum clique and maximum independent set—while exhibiting strong cross-problem transferability. Furthermore, the method provides effective warm starts for commercial solvers, significantly accelerating their convergence.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Combinatorial Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Unsupervised neural combinatorial optimization (NCO) offers an appealing alternative to supervised approaches by training learning-based solvers without ground-truth solutions, directly minimizing instance objectives and constraint violations. Yet for graph node subset-selection problems (e.g., Maximum Clique and Maximum Independent Set), existing unsupervised methods are typically specialized to a single problem class and rely on problem-specific surrogate losses, which hinders learning across classes within a unified framework. In this work, we propose UniHetCO, a unified heterogeneous graph representation for constrained quadratic programming-based combinatorial optimization that encodes problem structure, objective terms, and linear constraints in a single input. This formulation enables training a single model across multiple problem classes with a unified label-free objective. To improve stability under multi-problem learning, we employ a gradient-norm-based dynamic weighting scheme that alleviates gradient imbalance among classes. Experiments on multiple datasets and four constrained problem classes demonstrate competitive performance with state-of-the-art unsupervised NCO baselines, strong cross-problem adaptation potential, and effective warm starts for a commercial classical solver under tight time limits.

Problem

• unsupervised neural combinatorial optimization
• graph node subset-selection
• multi-problem learning
• unified framework
• heterogeneous representation

Innovation

• unified heterogeneous representation
• unsupervised neural combinatorial optimization
• multi-problem learning
• gradient-norm dynamic weighting
• constrained quadratic programming