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arXiv:2412.07216공식 코드 · Papers with Code

Learnable Sparse Customization in Heterogeneous Edge Computing

To effectively manage and utilize massive distributed data at the network edge, Federated Learning (FL) has emerged as a promising edge computing paradigm across data silos. However, FL still faces two challenges: system heterogeneity (i.e., the diversity of hardware resources across edge devices) and statistical heterogeneity (i.e., non-IID data). Although sparsification can extract diverse submodels for diverse clients, most sparse FL works either simply assign submodels with artificially-given rigid rules or prune partial parameters using heuristic strategies, resulting in inflexible sparsification and poor performance. In this work, we propose Learnable Personalized Sparsification for heterogeneous Federated learning (FedLPS), which achieves the learnable customization of heterogeneous sparse models with importance-associated patterns and adaptive ratios to simultaneously tackle system and statistical heterogeneity. Specifically, FedLPS learns the importance of model units on local data representation and further derives an importance-based sparse pattern with minimal heuristics to accurately extract personalized data features in non-IID settings. Furthermore, Prompt Upper Confidence Bound Variance (P-UCBV) is designed to adaptively determine sparse ratios by learning the superimposed effect of diverse device capabilities and non-IID data, aiming at resource self-adaptation with promising accuracy. Extensive experiments show that FedLPS outperforms status quo approaches in accuracy and training costs, which improves accuracy by 1.28%-59.34% while reducing running time by more than 68.80%.

arXiv:2412.05823공식 코드 · Papers with Code

DapperFL: Domain Adaptive Federated Learning with Model Fusion Pruning for Edge Devices

Federated learning (FL) has emerged as a prominent machine learning paradigm in edge computing environments, enabling edge devices to collaboratively optimize a global model without sharing their private data. However, existing FL frameworks suffer from efficacy deterioration due to the system heterogeneity inherent in edge computing, especially in the presence of domain shifts across local data. In this paper, we propose a heterogeneous FL framework DapperFL, to enhance model performance across multiple domains. In DapperFL, we introduce a dedicated Model Fusion Pruning (MFP) module to produce personalized compact local models for clients to address the system heterogeneity challenges. The MFP module prunes local models with fused knowledge obtained from both local and remaining domains, ensuring robustness to domain shifts. Additionally, we design a Domain Adaptive Regularization (DAR) module to further improve the overall performance of DapperFL. The DAR module employs regularization generated by the pruned model, aiming to learn robust representations across domains. Furthermore, we introduce a specific aggregation algorithm for aggregating heterogeneous local models with tailored architectures and weights. We implement DapperFL on a realworld FL platform with heterogeneous clients. Experimental results on benchmark datasets with multiple domains demonstrate that DapperFL outperforms several state-of-the-art FL frameworks by up to 2.28%, while significantly achieving model volume reductions ranging from 20% to 80%. Our code is available at: https://github.com/jyzgh/DapperFL.

arXiv:2412.01000공식 코드 · Papers with Code

Characterizing and Modeling AI-Driven Animal Ecology Studies at the Edge

Platforms that run artificial intelligence (AI) pipelines on edge computing resources are transforming the fields of animal ecology and biodiversity, enabling novel wildlife studies in animals' natural habitats. With emerging remote sensing hardware, e.g., camera traps and drones, and sophisticated AI models in situ, edge computing will be more significant in future AI-driven animal ecology (ADAE) studies. However, the study's objectives, the species of interest, its behaviors, range, habitat, and camera placement affect the demand for edge resources at runtime. If edge resources are under-provisioned, studies can miss opportunities to adapt the settings of camera traps and drones to improve the quality and relevance of captured data. This paper presents salient features of ADAE studies that can be used to model latency, throughput objectives, and provision edge resources. Drawing from studies that span over fifty animal species, four geographic locations, and multiple remote sensing methods, we characterized common patterns in ADAE studies, revealing increasingly complex workflows involving various computer vision tasks with strict service level objectives (SLO). ADAE workflow demands will soon exceed individual edge devices' compute and memory resources, requiring multiple networked edge devices to meet performance demands. We developed a framework to scale traces from prior studies and replay them offline on representative edge platforms, allowing us to capture throughput and latency data across edge configurations. We used the data to calibrate queuing and machine learning models that predict performance on unseen edge configurations, achieving errors as low as 19%.

arXiv:2411.18009공식 코드 · Papers with Code

Monocular Obstacle Avoidance Based on Inverse PPO for Fixed-wing UAVs

Fixed-wing Unmanned Aerial Vehicles (UAVs) are one of the most commonly used platforms for the burgeoning Low-altitude Economy (LAE) and Urban Air Mobility (UAM), due to their long endurance and high-speed capabilities. Classical obstacle avoidance systems, which rely on prior maps or sophisticated sensors, face limitations in unknown low-altitude environments and small UAV platforms. In response, this paper proposes a lightweight deep reinforcement learning (DRL) based UAV collision avoidance system that enables a fixed-wing UAV to avoid unknown obstacles at cruise speed over 30m/s, with only onboard visual sensors. The proposed system employs a single-frame image depth inference module with a streamlined network architecture to ensure real-time obstacle detection, optimized for edge computing devices. After that, a reinforcement learning controller with a novel reward function is designed to balance the target approach and flight trajectory smoothness, satisfying the specific dynamic constraints and stability requirements of a fixed-wing UAV platform. An adaptive entropy adjustment mechanism is introduced to mitigate the exploration-exploitation trade-off inherent in DRL, improving training convergence and obstacle avoidance success rates. Extensive software-in-the-loop and hardware-in-the-loop experiments demonstrate that the proposed framework outperforms other methods in obstacle avoidance efficiency and flight trajectory smoothness and confirm the feasibility of implementing the algorithm on edge devices. The source code is publicly available at \url{https://github.com/ch9397/FixedWing-MonoPPO}.

arXiv:2411.11857공식 코드 · Papers with Code

Radiance Field Delta Video Compression in Edge-Enabled Vehicular Metaverse

Connected and autonomous vehicles (CAVs) offload computationally intensive tasks to multi-access edge computing (MEC) servers via vehicle-to-infrastructure (V2I) communication, enabling applications within the vehicular metaverse, which transforms physical environment into the digital space enabling advanced analysis or predictive modeling. A core challenge is physical-to-virtual (P2V) synchronization through digital twins (DTs), reliant on MEC networks and ultra-reliable low-latency communication (URLLC). To address this, we introduce radiance field (RF) delta video compression (RFDVC), which uses RF-encoder and RF-decoder architecture using distributed RFs as DTs storing photorealistic 3D urban scenes in compressed form. This method extracts differences between CAV-frame capturing actual traffic and RF-frame capturing empty scene from the same camera pose in batches encoded and transmitted over the MEC network. Experiments show data savings up to 71% against H.264 codec and 44% against H.265 codec under different conditions as lighting changes, and rain. RFDVC also demonstrates resilience to transmission errors, achieving up to +0.29 structural similarity index measure (SSIM) improvement at block error rate (BLER) = 0.35 in non-rainy and +0.25 at BLER = 0.2 in rainy conditions, ensuring superior visual quality compared to standard video coding (VC) methods across various conditions.

arXiv:2411.03835공식 코드 · Papers with Code

An Edge Computing-Based Solution for Real-Time Leaf Disease Classification using Thermal Imaging

Deep learning (DL) technologies can transform agriculture by improving crop health monitoring and management, thus improving food safety. In this paper, we explore the potential of edge computing for real-time classification of leaf diseases using thermal imaging. We present a thermal image dataset for plant disease classification and evaluate deep learning models, including InceptionV3, MobileNetV1, MobileNetV2, and VGG-16, on resource-constrained devices like the Raspberry Pi 4B. Using pruning and quantization-aware training, these models achieve inference times up to 1.48x faster on Edge TPU Max for VGG16, and up to 2.13x faster with precision reduction on Intel NCS2 for MobileNetV1, compared to high-end GPUs like the RTX 3090, while maintaining state-of-the-art accuracy.

arXiv:2409.18999공식 코드 · Papers with Code

Enhancing TinyBERT for Financial Sentiment Analysis Using GPT-Augmented FinBERT Distillation

In the rapidly evolving field of financial sentiment analysis, the efficiency and accuracy of predictive models are critical due to their significant impact on financial markets. Transformer based models like BERT and large language models (LLMs) like GPT-4, have advanced NLP tasks considerably. Despite their advantages, BERT-based models face challenges with computational intensity in edge computing environments, and the substantial size and compute requirements of LLMs limit their practical deployment. This study proposes leveraging the generative capabilities of LLMs, such as GPT-4 Omni, to create synthetic, domain-specific training data. This approach addresses the challenge of data scarcity and enhances the performance of smaller models by making them competitive with their larger counterparts. The research specifically aims to enhance FinBERT, a BERT model fine-tuned for financial sentiment analysis, and develop TinyFinBERT, a compact transformer model, through a structured, two-tiered knowledge distillation strategy. Using data augmented by GPT-4 Omni, which involves generating new training examples and transforming existing data, we significantly improved the accuracy of FinBERT, preparing it to serve as a teacher model. This enhanced FinBERT then distilled knowledge to TinyFinBERT, employing both GPT-4 Omni and GPT-3.5 Turbo augmented data. The distillation strategy incorporated both logit and intermediate layer distillation. The training and evaluation of TinyFinBERT utilized the PhraseBank dataset and the FiQA 2018 Task1 dataset, achieving performance comparable to FinBERT while being substantially smaller and more efficient. This research demonstrates how LLMs can effectively contribute to the advancement of financial sentiment analysis by enhancing the capabilities of smaller, more efficient models through innovative data augmentation and distillation techniques.

arXiv:2410.11112공식 코드 · Papers with Code

Differentiable Weightless Neural Networks

We introduce the Differentiable Weightless Neural Network (DWN), a model based on interconnected lookup tables. Training of DWNs is enabled by a novel Extended Finite Difference technique for approximate differentiation of binary values. We propose Learnable Mapping, Learnable Reduction, and Spectral Regularization to further improve the accuracy and efficiency of these models. We evaluate DWNs in three edge computing contexts: (1) an FPGA-based hardware accelerator, where they demonstrate superior latency, throughput, energy efficiency, and model area compared to state-of-the-art solutions, (2) a low-power microcontroller, where they achieve preferable accuracy to XGBoost while subject to stringent memory constraints, and (3) ultra-low-cost chips, where they consistently outperform small models in both accuracy and projected hardware area. DWNs also compare favorably against leading approaches for tabular datasets, with higher average rank. Overall, our work positions DWNs as a pioneering solution for edge-compatible high-throughput neural networks.

arXiv:2408.15800공식 코드 · Papers with Code

Emulating Brain-like Rapid Learning in Neuromorphic Edge Computing

Achieving personalized intelligence at the edge with real-time learning capabilities holds enormous promise in enhancing our daily experiences and helping decision making, planning, and sensing. However, efficient and reliable edge learning remains difficult with current technology due to the lack of personalized data, insufficient hardware capabilities, and inherent challenges posed by online learning. Over time and across multiple developmental stages, the brain has evolved to efficiently incorporate new knowledge by gradually building on previous knowledge. In this work, we emulate the multiple stages of learning with digital neuromorphic technology that simulates the neural and synaptic processes of the brain using two stages of learning. First, a meta-training stage trains the hyperparameters of synaptic plasticity for one-shot learning using a differentiable simulation of the neuromorphic hardware. This meta-training process refines a hardware local three-factor synaptic plasticity rule and its associated hyperparameters to align with the trained task domain. In a subsequent deployment stage, these optimized hyperparameters enable fast, data-efficient, and accurate learning of new classes. We demonstrate our approach using event-driven vision sensor data and the Intel Loihi neuromorphic processor with its plasticity dynamics, achieving real-time one-shot learning of new classes that is vastly improved over transfer learning. Our methodology can be deployed with arbitrary plasticity models and can be applied to situations demanding quick learning and adaptation at the edge, such as navigating unfamiliar environments or learning unexpected categories of data through user engagement.

arXiv:2408.14831공식 코드 · Papers with Code

DRL-Based Federated Self-Supervised Learning for Task Offloading and Resource Allocation in ISAC-Enabled Vehicle Edge Computing

Intelligent Transportation Systems (ITS) leverage Integrated Sensing and Communications (ISAC) to enhance data exchange between vehicles and infrastructure in the Internet of Vehicles (IoV). This integration inevitably increases computing demands, risking real-time system stability. Vehicle Edge Computing (VEC) addresses this by offloading tasks to Road Side Unit (RSU), ensuring timely services. Our previous work FLSimCo algorithm, which uses local resources for Federated Self-Supervised Learning (SSL), though vehicles often can't complete all iterations task. Our improved algorithm offloads partial task to RSU and optimizes energy consumption by adjusting transmission power, CPU frequency, and task assignment ratios, balancing local and RSU-based training. Meanwhile, setting an offloading threshold further prevents inefficiencies. Simulation results show that the enhanced algorithm reduces energy consumption, improves offloading efficiency and the accuracy of Federated SSL.

arXiv:2408.14947공식 코드 · Papers with Code

ERX: A Fast Real-Time Anomaly Detection Algorithm for Hyperspectral Line Scanning

Detecting unexpected objects (anomalies) in real time has great potential for monitoring, managing, and protecting the environment. Hyperspectral line-scan cameras are a low-cost solution that enhance confidence in anomaly detection over RGB and multispectral imagery. However, existing line-scan algorithms are too slow when using small computers (e.g. those onboard a drone or small satellite), do not adapt to changing scenery, or lack robustness against geometric distortions. This paper introduces the Exponentially moving RX algorithm (ERX) to address these issues, and compares it with four existing RX-based anomaly detection methods for hyperspectral line scanning. Three large and more complex datasets are also introduced to better assess the practical challenges when using line-scan cameras (two hyperspectral and one multispectral). ERX was evaluated using a Jetson Xavier NX edge computing module (6-core CPU, 8GB RAM, 20W power draw), achieving the best combination of speed and detection performance. ERX was 9 times faster than the next-best algorithm on the dataset with the highest number of bands (108 band), with an average speed of 561 lines per second on the Jetson. It achieved a 29.3% AUC improvement over the next-best algorithm on the most challenging dataset, while showing greater adaptability through consistently high AUC scores regardless of the camera's starting location. ERX performed robustly across all datasets, achieving an AUC of 0.941 on a drone-collected hyperspectral line scan dataset without geometric corrections (a 16.9% improvement over existing algorithms). This work enables future research on the detection of anomalous objects in real time, adaptive and automatic threshold selection, and real-time field tests. The datasets and the Python code are openly available at: https://github.com/WiseGamgee/HyperAD, promoting accessibility and future work.

arXiv:2408.05617공식 코드 · Papers with Code

Residual-INR: Communication Efficient On-Device Learning Using Implicit Neural Representation

Edge computing is a distributed computing paradigm that collects and processes data at or near the source of data generation. The on-device learning at edge relies on device-to-device wireless communication to facilitate real-time data sharing and collaborative decision-making among multiple devices. This significantly improves the adaptability of the edge computing system to the changing environments. However, as the scale of the edge computing system is getting larger, communication among devices is becoming the bottleneck because of the limited bandwidth of wireless communication leads to large data transfer latency. To reduce the amount of device-to-device data transmission and accelerate on-device learning, in this paper, we propose Residual-INR, a fog computing-based communication-efficient on-device learning framework by utilizing implicit neural representation (INR) to compress images/videos into neural network weights. Residual-INR enhances data transfer efficiency by collecting JPEG images from edge devices, compressing them into INR format at the fog node, and redistributing them for on-device learning. By using a smaller INR for full image encoding and a separate object INR for high-quality object region reconstruction through residual encoding, our technique can reduce the encoding redundancy while maintaining the object quality. Residual-INR is a promising solution for edge on-device learning because it reduces data transmission by up to 5.16 x across a network of 10 edge devices. It also facilitates CPU-free accelerated on-device learning, achieving up to 2.9 x speedup without sacrificing accuracy. Our code is available at: https://github.com/sharc-lab/Residual-INR.

arXiv:2407.20124공식 코드 · Papers with Code

AxiomVision: Accuracy-Guaranteed Adaptive Visual Model Selection for Perspective-Aware Video Analytics

The rapid evolution of multimedia and computer vision technologies requires adaptive visual model deployment strategies to effectively handle diverse tasks and varying environments. This work introduces AxiomVision, a novel framework that can guarantee accuracy by leveraging edge computing to dynamically select the most efficient visual models for video analytics under diverse scenarios. Utilizing a tiered edge-cloud architecture, AxiomVision enables the deployment of a broad spectrum of visual models, from lightweight to complex DNNs, that can be tailored to specific scenarios while considering camera source impacts. In addition, AxiomVision provides three core innovations: (1) a dynamic visual model selection mechanism utilizing continual online learning, (2) an efficient online method that efficiently takes into account the influence of the camera's perspective, and (3) a topology-driven grouping approach that accelerates the model selection process. With rigorous theoretical guarantees, these advancements provide a scalable and effective solution for visual tasks inherent to multimedia systems, such as object detection, classification, and counting. Empirically, AxiomVision achieves a 25.7\% improvement in accuracy.

arXiv:2407.13123공식 코드 · Papers with Code

Reconfigurable Intelligent Surface Aided Vehicular Edge Computing: Joint Phase-shift Optimization and Multi-User Power Allocation

Vehicular edge computing (VEC) is an emerging technology with significant potential in the field of internet of vehicles (IoV), enabling vehicles to perform intensive computational tasks locally or offload them to nearby edge devices. However, the quality of communication links may be severely deteriorated due to obstacles such as buildings, impeding the offloading process. To address this challenge, we introduce the use of Reconfigurable Intelligent Surfaces (RIS), which provide alternative communication pathways to assist vehicular communication. By dynamically adjusting the phase-shift of the RIS, the performance of VEC systems can be substantially improved. In this work, we consider a RIS-assisted VEC system, and design an optimal scheme for local execution power, offloading power, and RIS phase-shift, where random task arrivals and channel variations are taken into account. To address the scheme, we propose an innovative deep reinforcement learning (DRL) framework that combines the Deep Deterministic Policy Gradient (DDPG) algorithm for optimizing RIS phase-shift coefficients and the Multi-Agent Deep Deterministic Policy Gradient (MADDPG) algorithm for optimizing the power allocation of vehicle user (VU). Simulation results show that our proposed scheme outperforms the traditional centralized DDPG, Twin Delayed Deep Deterministic Policy Gradient (TD3) and some typical stochastic schemes.

arXiv:2407.12980공식 코드 · Papers with Code

A Framework for testing Federated Learning algorithms using an edge-like environment

Federated Learning (FL) is a machine learning paradigm in which many clients cooperatively train a single centralized model while keeping their data private and decentralized. FL is commonly used in edge computing, which involves placing computer workloads (both hardware and software) as close as possible to the edge, where the data is being created and where actions are occurring, enabling faster response times, greater data privacy, and reduced data transfer costs. However, due to the heterogeneous data distributions/contents of clients, it is non-trivial to accurately evaluate the contributions of local models in global centralized model aggregation. This is an example of a major challenge in FL, commonly known as data imbalance or class imbalance. In general, testing and assessing FL algorithms can be a very difficult and complex task due to the distributed nature of the systems. In this work, a framework is proposed and implemented to assess FL algorithms in a more easy and scalable way. This framework is evaluated over a distributed edge-like environment managed by a container orchestration platform (i.e. Kubernetes).

arXiv:2407.12605공식 코드 · Papers with Code

Continuous reasoning for adaptive container image distribution in the cloud-edge continuum

Cloud-edge computing requires applications to operate across diverse infrastructures, often triggered by cyber-physical events. Containers offer a lightweight deployment option but pulling images from central repositories can cause delays. This article presents a novel declarative approach and open-source prototype for replicating container images across the cloud-edge continuum. Considering resource availability, network QoS, and storage costs, we leverage logic programming to (i) determine optimal initial placements via Answer Set Programming (ASP) and (ii) adapt placements using Prolog-based continuous reasoning. We evaluate our solution through simulations, showcasing how combining ASP and Prolog continuous reasoning can balance cost optimisation and prompt decision-making in placement adaptation at increasing infrastructure sizes.

arXiv:2407.11310공식 코드 · Papers with Code

Digital Twin Vehicular Edge Computing Network: Task Offloading and Resource Allocation

With the increasing demand for multiple applications on internet of vehicles. It requires vehicles to carry out multiple computing tasks in real time. However, due to the insufficient computing capability of vehicles themselves, offloading tasks to vehicular edge computing (VEC) servers and allocating computing resources to tasks becomes a challenge. In this paper, a multi task digital twin (DT) VEC network is established. By using DT to develop offloading strategies and resource allocation strategies for multiple tasks of each vehicle in a single slot, an optimization problem is constructed. To solve it, we propose a multi-agent reinforcement learning method on the task offloading and resource allocation. Numerous experiments demonstrate that our method is effective compared to other benchmark algorithms.

arXiv:2407.07575공식 코드 · Papers with Code

Resource Allocation for Twin Maintenance and Computing Task Processing in Digital Twin Vehicular Edge Computing Network

As a promising technology, vehicular edge computing (VEC) can provide computing and caching services by deploying VEC servers near vehicles. However, VEC networks still face challenges such as high vehicle mobility. Digital twin (DT), an emerging technology, can predict, estimate, and analyze real-time states by digitally modeling objects in the physical world. By integrating DT with VEC, a virtual vehicle DT can be created in the VEC server to monitor the real-time operating status of vehicles. However, maintaining the vehicle DT model requires ongoing attention from the VEC server, which also needs to offer computing services for the vehicles. Therefore, effective allocation and scheduling of VEC server resources are crucial. This study focuses on a general VEC network with a single VEC service and multiple vehicles, examining the two types of delays caused by twin maintenance and computational processing within the network. By transforming the problem using satisfaction functions, we propose an optimization problem aimed at maximizing each vehicle's resource utility to determine the optimal resource allocation strategy. Given the non-convex nature of the issue, we employ multi-agent Markov decision processes to reformulate the problem. Subsequently, we propose the twin maintenance and computing task processing resource collaborative scheduling (MADRL-CSTC) algorithm, which leverages multi-agent deep reinforcement learning. Through experimental comparisons with alternative algorithms, it demonstrates that our proposed approach is effective in terms of resource allocation.

arXiv:2407.05633공식 코드 · Papers with Code

AdaPI: Facilitating DNN Model Adaptivity for Efficient Private Inference in Edge Computing

Private inference (PI) has emerged as a promising solution to execute computations on encrypted data, safeguarding user privacy and model parameters in edge computing. However, existing PI methods are predominantly developed considering constant resource constraints, overlooking the varied and dynamic resource constraints in diverse edge devices, like energy budgets. Consequently, model providers have to design specialized models for different devices, where all of them have to be stored on the edge server, resulting in inefficient deployment. To fill this gap, this work presents AdaPI, a novel approach that achieves adaptive PI by allowing a model to perform well across edge devices with diverse energy budgets. AdaPI employs a PI-aware training strategy that optimizes the model weights alongside weight-level and feature-level soft masks. These soft masks are subsequently transformed into multiple binary masks to enable adjustments in communication and computation workloads. Through sequentially training the model with increasingly dense binary masks, AdaPI attains optimal accuracy for each energy budget, which outperforms the state-of-the-art PI methods by 7.3\% in terms of test accuracy on CIFAR-100. The code of AdaPI can be accessed via https://github.com/jiahuiiiiii/AdaPI.

arXiv:2407.02342공식 코드 · Papers with Code

Optimizing Age of Information in Vehicular Edge Computing with Federated Graph Neural Network Multi-Agent Reinforcement Learning

With the rapid development of intelligent vehicles and Intelligent Transport Systems (ITS), the sensors such as cameras and LiDAR installed on intelligent vehicles provides higher capacity of executing computation-intensive and delay-sensitive tasks, thereby raising deployment costs. To address this issue, Vehicular Edge Computing (VEC) has been proposed to process data through Road Side Units (RSUs) to support real-time applications. This paper focuses on the Age of Information (AoI) as a key metric for data freshness and explores task offloading issues for vehicles under RSU communication resource constraints. We adopt a Multi-agent Deep Reinforcement Learning (MADRL) approach, allowing vehicles to autonomously make optimal data offloading decisions. However, MADRL poses risks of vehicle information leakage during communication learning and centralized training. To mitigate this, we employ a Federated Learning (FL) framework that shares model parameters instead of raw data to protect the privacy of vehicle users. Building on this, we propose an innovative distributed federated learning framework combining Graph Neural Networks (GNN), named Federated Graph Neural Network Multi-Agent Reinforcement Learning (FGNN-MADRL), to optimize AoI across the system. For the first time, road scenarios are constructed as graph data structures, and a GNN-based federated learning framework is proposed, effectively combining distributed and centralized federated aggregation. Furthermore, we propose a new MADRL algorithm that simplifies decision making and enhances offloading efficiency, further reducing the decision complexity. Simulation results demonstrate the superiority of our proposed approach to other methods through simulations.