DiffSG: A Generative Solver for Network Optimization with Diffusion Model

2024-08-13

arXiv.org

AI Summary

This work addresses challenging network optimization problems—including mixed-integer nonlinear programming (MINLP), convex, and hierarchical nonconvex optimization—by proposing DiffSG, the first framework to directly apply generative diffusion models to network optimization. DiffSG overcomes the limitations of discriminative models (e.g., single-step mapping and local search) by modeling the implicit distribution of high-quality solutions, enabling global-aware, multi-step progressive optimization. Methodologically, it innovatively integrates distribution learning, iterative denoising sampling, and structural adaptation to MINLP constraints, providing a unified treatment for both convex and nonconvex formulations. Extensive experiments demonstrate that DiffSG consistently outperforms state-of-the-art baselines across diverse network optimization tasks, achieving superior in-domain performance and strong cross-domain generalization capability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Generative diffusion models, famous for their performance in image generation, are popular in various cross-domain applications. However, their use in the communication community has been mostly limited to auxiliary tasks like data modeling and feature extraction. These models hold greater promise for fundamental problems in network optimization compared to traditional machine learning methods. Discriminative deep learning often falls short due to its single-step input-output mapping and lack of global awareness of the solution space, especially given the complexity of network optimization's objective functions. In contrast, generative diffusion models can consider a broader range of solutions and exhibit stronger generalization by learning parameters that describe the distribution of the underlying solution space, with higher probabilities assigned to better solutions. We propose a new framework Diffusion Model-based Solution Generation (DiffSG), which leverages the intrinsic distribution learning capabilities of generative diffusion models to learn high-quality solution distributions based on given inputs. The optimal solution within this distribution is highly probable, allowing it to be effectively reached through repeated sampling. We validate the performance of DiffSG on several typical network optimization problems, including mixed-integer non-linear programming, convex optimization, and hierarchical non-convex optimization. Our results demonstrate that DiffSG outperforms existing baseline methods not only on in-domain inputs but also on out-of-domain inputs. In summary, we demonstrate the potential of generative diffusion models in tackling complex network optimization problems and outline a promising path for their broader application in the communication community. Our code is available at https://github.com/qiyu3816/DiffSG.

Problem

• Leverages generative diffusion models for network optimization.
• Addresses limitations of discriminative deep learning in optimization.
• Validates performance on complex network optimization problems.

Innovation

• DiffSG uses generative diffusion models for network optimization.
• It learns high-quality solution distributions from inputs.
• DiffSG outperforms traditional methods in complex optimizations.