Stein Variational Black-Box Combinatorial Optimization

2026-04-17

AI Summary

This work addresses the challenge of premature convergence to a single optimum in high-dimensional combinatorial black-box optimization, where balancing exploration and exploitation remains difficult. The authors propose the first integration of Stein variational gradient descent into estimation-of-distribution algorithms, introducing a repulsive mechanism among particles in the parameter space to drive the population toward collaborative exploration of multiple fitness peaks. This approach significantly enhances multimodal search capability, achieving performance that matches or surpasses state-of-the-art algorithms across a range of benchmark problems, with particularly notable improvements on large-scale instances.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Combinatorial black-box optimization in high-dimensional settings demands a careful trade-off between exploiting promising regions of the search space and preserving sufficient exploration to identify multiple optima. Although Estimation-of-Distribution Algorithms (EDAs) provide a powerful model-based framework, they often concentrate on a single region of interest, which may result in premature convergence when facing complex or multimodal objective landscapes. In this work, we incorporate the Stein operator to introduce a repulsive mechanism among particles in the parameter space, thereby encouraging the population to disperse and jointly explore several modes of the fitness landscape. Empirical evaluations across diverse benchmark problems show that the proposed method achieves performance competitive with, and in several cases superior to, leading state-of-the-art approaches, particularly on large-scale instances. These findings highlight the potential of Stein variational gradient descent as a promising direction for addressing large, computationally expensive, discrete black-box optimization problems.

Problem

• combinatorial optimization
• black-box optimization
• multimodal optimization
• premature convergence
• high-dimensional optimization

Innovation

• Stein variational gradient descent
• combinatorial optimization
• black-box optimization
• repulsive mechanism
• estimation-of-distribution algorithms