SeLR: Sparsity-enhanced Lagrangian Relaxation for Computation Offloading at the Edge

2025-05-01

AI Summary

This paper addresses the offloading optimization problem for sensor data processing tasks in edge networks, jointly optimizing server selection, transmission routing, and service configuration to achieve Pareto-optimal trade-offs between accuracy and task completion time. The problem is formulated as a non-convex, NP-hard mixed-integer program (MIP). To tackle it, we propose an iterative convex optimization framework that integrates Lagrangian duality to penalize constraint violations, employs reweighted ℓ₁ sparsity regularization to enhance solution quality and convergence, and leverages continuous relaxation with primal-dual updates for efficient computation. Evaluations on a 300-node hierarchical edge network demonstrate that our approach reduces scheduling overhead by 7.72–9.17× compared to commercial MIP solvers, yields a significantly superior Pareto frontier versus greedy heuristics, and scales effectively to hundreds of concurrent tasks.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper introduces a novel computational approach for offloading sensor data processing tasks to servers in edge networks for better accuracy and makespan. A task is assigned with one of several offloading options, each comprises a server, a route for uploading data to the server, and a service profile that specifies the performance and resource consumption at the server and in the network. This offline offloading and routing problem is formulated as mixed integer programming (MIP), which is non-convex and HP-hard due to the discrete decision variables associated to the offloading options. The novelty of our approach is to transform this non-convex problem into iterative convex optimization by relaxing integer decision variables into continuous space, combining primal-dual optimization for penalizing constraint violations and reweighted $L_1$-minimization for promoting solution sparsity, which achieves better convergence through a smoother path in a continuous search space. Compared to existing greedy heuristics, our approach can achieve a better Pareto frontier in accuracy and latency, scales better to larger problem instances, and can achieve a 7.72--9.17$ imes$ reduction in computational overhead of scheduling compared to the optimal solver in hierarchically organized edge networks with 300 nodes and 50--100 tasks.

Problem

• Optimizing sensor data offloading to edge servers for accuracy and latency
• Transforming non-convex MIP into iterative convex optimization via sparsity
• Reducing computational overhead in large-scale edge networks

Innovation

• Transforms non-convex MIP into iterative convex optimization
• Combines primal-dual optimization with reweighted L1-minimization
• Enhances sparsity for better convergence in continuous space