An Optimisation Approach for Edge Computing Task Offloading Based on Hermes Algorithm and Reinforcement Learning

Mobile Edge Computing (MEC) alleviates enddevice constraints by offloading computation to nearby edge servers, thereby reducing task latency and energy. We present Hermes-RL, a two-stage offloading method: a Hermes-style FPTAS first provides an initial task-to-node mapping with a $(1+\varepsilon)$ approximation guarantee under static parameters; a tabular Qlearning agent then updates decisions online as bandwidth and server load vary. We model DAG workflows and use a reward that combines delay and energy with penalties for overload and deadline violations. In simulation, Hermes-RL attains the second-lowest end-to-end latency-close to Cloud-First, which benefits from high compute speed despite communication over-head-and approaches that latency by selectively offloading when transmissions are worthwhile. As a result, Hermes-RL achieves a more favourable latency-energy balance than static Hermes, Random, and standalone Q-learning. Initialising with Hermes reduces exploration and shortens empirical convergence.