Diffusion Models as Network Optimizers: Explorations and Analysis

Network optimization is a fundamental challenge in the Internet of Things (IoT) network, often characterized by complex features that make it difficult to solve these problems. Recently, generative diffusion models (GDMs) have emerged as a promising new approach to network optimization, with the potential to directly address these optimization problems. However, the application of GDMs in this field is still in its early stages, and there is a noticeable lack of theoretical research and empirical findings. In this study, we first explore the intrinsic characteristics of generative models. Next, we provide a concise theoretical proof and intuitive demonstration of the advantages of generative models over discriminative models in network optimization. Based on this exploration, we implement GDMs as optimizers aimed at learning high-quality solution distributions for given inputs, sampling from these distributions during inference to approximate or achieve optimal solutions. Specifically, we utilize denoising diffusion probabilistic models (DDPMs) and employ a classifier-free guidance mechanism to manage conditional guidance based on input parameters. We conduct extensive experiments across three challenging network optimization problems. By investigating various model configurations and the principles of GDMs as optimizers, we demonstrate the ability to overcome prediction errors and validate the convergence of generated solutions to optimal solutions.We provide code and data at https://github.com/qiyu3816/DiffSG.

DiffSG: A Generative Solver for Network Optimization with Diffusion Model

Diffusion generative 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, diffusion generative 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 diffusion generative 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 show that DiffSG outperforms existing baselines. In summary, we demonstrate the potential of diffusion generative models in tackling complex network optimization problems and outline a promising path for their broader application in the communication community.

A Multi-Head Ensemble Multi-Task Learning Approach for Dynamical Computation Offloading

Computation offloading has become a popular solution to support computationally intensive and latency-sensitive applications by transferring computing tasks to mobile edge servers (MESs) for execution, which is known as mobile/multi-access edge computing (MEC). To improve the MEC performance, it is required to design an optimal offloading strategy that includes offloading decision (i.e., whether offloading or not) and computational resource allocation of MEC. The design can be formulated as a mixed-integer nonlinear programming (MINLP) problem, which is generally NP-hard and its effective solution can be obtained by performing online inference through a well-trained deep neural network (DNN) model. However, when the system environments change dynamically, the DNN model may lose efficacy due to the drift of input parameters, thereby decreasing the generalization ability of the DNN model. To address this unique challenge, in this paper, we propose a multi-head ensemble multi-task learning (MEMTL) approach with a shared backbone and multiple prediction heads (PHs). Specifically, the shared backbone will be invariant during the PHs training and the inferred results will be ensembled, thereby significantly reducing the required training overhead and improving the inference performance. As a result, the joint optimization problem for offloading decision and resource allocation can be efficiently solved even in a time-varying wireless environment. Experimental results show that the proposed MEMTL outperforms benchmark methods in both the inference accuracy and mean square error without requiring additional training data.