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

TL;DR

This work tackles offline joint task offloading and routing in multi-hop edge networks, formulating it as a non-convex MIP with binary decisions. It introduces Sparsity-enhanced Lagrangian Relaxation (SeLR), which combines reweighted $L_1$-minimization and primal-dual optimization to transform the problem into an iterative sequence of convex problems while promoting sparse, near-binary solutions. Through RL1 and dual ascent, SeLR achieves better scalability and closer-to-optimal Pareto frontiers in accuracy vs. latency than greedy heuristics, with substantially lower scheduling overhead than the exact MIP solver on networks of ~300 nodes and 50–100 tasks. The approach is validated on simulated tactical edge networks, showing favorable trade-offs and highlighting potential extensions with graph-based learning to further reduce optimality gaps.

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$\times$ reduction in computational overhead of scheduling compared to the optimal solver in hierarchically organized edge networks with 300 nodes and 50--100 tasks.

Figures (6)

• Figure 1: Illustration of the simplified network topology, highlighting the connections between servers and sensors in our setup. Offloading Options for each task are selected based on the network topology, taking into account the max-hop limitation, edge bandwidth, and the tasks' accuracy and latency requirements, as outlined in Algorithm \ref{['alg:rworkflow_construction']}.
• Figure 2: Utility value distribution for Greedy-T with 100 random order permutations compared to the Optimal utility value for task loads of 30, 60, and 100. The Greedy-T$\times100$ chooses the closest outcome to the Optimal utility. The utility function is based on $\lambda = 0.5$.
• Figure 3: Normalized total utility achieved by the evaluated schedulers as a function of the number of tasks $|{\mathcal{T}}|$, relative to the optimal solution, with $\lambda = 0.5$. Each curve represents an average over 30 network instances with $|\mathcal{V}| = 300$. On each network instance, tasks are added incrementally such that the test instance for $|{\mathcal{T}}| = N+1$ always includes the same set of tasks in the instance with $|{\mathcal{T}}| = N$ .
• Figure 4: Accuracy vs. latency curve for all schemes as a function of gradually increasing $\lambda$ values from 0 to 1. Results are shown for $\lambda \in \{0.1, 0.15, 0.4, 0.6, 0.8\}$, with larger markers indicating higher $\lambda$ values, for task loads of 75 and 100, averaged over 30 network instances with a size of $\mathcal{V} = 300$. For Greedy-U, Greedy-T, and Greedy-T$\times100$, the markers of $\lambda=0.6$ and $\lambda=0.8$ overlap.
• Figure 5: The numbers of on-device task assignments under tested schedulers as the CPU capacities of all nodes scaled by a factor of $\beta\in\{0.5, 0.75, 1, 1.25, 1.5\}$, with other resources such as RAM and bandwidth remaining the same. Workloads $|{\mathcal{T}}|\in\{30,60,90\}$, and $\lambda = 0.5$. The results are averaged over 30 network instances with $\mathcal{V} = 300$ nodes.