Cross-Problem Solving for Network Optimization: Is Problem-Aware Learning the Key?

TL;DR

This work tackles the challenge of cross-problem generalization in edge-network optimization by introducing PAD, a problem-aware diffusion framework that encodes optimization problem formulations as token-level embeddings. A rank-pooling strategy extracts fixed-length, information-rich problem representations, which condition a latent diffusion model to generate solutions across unseen problems, while a constraint-aware module improves feasibility during training. Through experiments on ten diverse network optimization problems, PAD demonstrates robust generalization to new tasks and competitive performance with traditional solvers, while offering substantial efficiency advantages over large language-model-based approaches. The study also shows that clustering problems by mathematical structure and careful training problem selection further enhances cross-problem transfer, pointing to a scalable path toward general-purpose solvers for intelligent network operation and resource management.

Abstract

As intelligent network services continue to diversify, ensuring efficient and adaptive resource allocation in edge networks has become increasingly critical. Yet the wide functional variations across services often give rise to new and unforeseen optimization problems, rendering traditional manual modeling and solver design both time-consuming and inflexible. This limitation reveals a key gap between current methods and human solving - the inability to recognize and understand problem characteristics. It raises the question of whether problem-aware learning can bridge this gap and support effective cross-problem generalization. To answer this question, we propose a problem-aware diffusion (PAD) model, which leverages a problem-aware learning framework to enable cross-problem generalization. By explicitly encoding the mathematical formulations of optimization problems into token-level embeddings, PAD empowers the model to understand and adapt to problem structures. Extensive experiments across ten representative network optimization problems show that PAD generalizes well to unseen problems while avoiding the inefficiency of building new solvers from scratch, yet still delivering competitive solution quality. Meanwhile, an auxiliary constraint-aware module is designed to enforce solution validity further. The experiments indicate that problem-aware learning opens a promising direction toward general-purpose solvers for intelligent network operation and resource management. Our code is open source at https://github.com/qiyu3816/PAD.

Figures (9)

• Figure 1: Comparison of PAD with other isolated methods for cross-problem network optimization. PAD trains once and adapts to new problems by explicitly inputting $\mathbb{P}_i$ from formulation embedding, whereas traditional methods require re-training, even redesigning, for each individual problem.
• Figure 2: Implementation framework of PAD.
• Figure 3: Neural network structure of PAD.
• Figure 4: Comparison of different pooling methods on GT_GAP $\downarrow$ and CONS_IF $\uparrow$. The three subplots correspond to the three pooling lengths. Yellow markers represent GT_GAP (measured on the left y-axis), while blue markers represent CONS_IF (measured on the right y-axis).
• Figure 5: Comparison of different pooling lengths on GT_GAP $\downarrow$ and CONS_IF $\uparrow$. The three subplots correspond to the three pooling methods. Yellow markers represent GT_GAP (measured on the left y-axis), while blue markers represent CONS_IF (measured on the right y-axis).