Computing efficiency and latency optimization in intelligent reflecting surface-enhanced device-to-device mobile edge computing via lagrange-dual deep learning

In this work, we investigate device-to-device (D2D) mobile edge computing (MEC) with intelligent reflecting surface (IRS) aiding both D2D and device-to-MEC links to reduce energy and delay for user devices. We formulate a non-convex computation offloading problem that maximizes computing efficiency over latency under mixed integer, linear, and non-linear constraints and jointly optimize offloading decisions, partial offloading ratio, edge computing frequency, transmit power, and IRS phase shifts via a fully connected deep neural network (DNN) trained with a Lagrange-dual loss function that embeds the objective and inequality constraints. Extensive simulations across varying maximum task sizes (0.5-3 Mbits), edge computing capacities (10-90 Mcycles/s), and number of IRS elements (10-30) show that the proposed method consistently achieves solutions within 5-10% of near-global optimal solutions obtained by exhaustive search (ES) and outperforms gradient search (GS), fixed-offloading DNN and REINFORCE algorithm that achieves approximately 50% higher computing efficiency at $$N_1=20$$ users. The proposed DNN exhibits 3-5% energy consumption gap from ES while maintaining lower computational complexity of $$O(12N_cN^2Ms)$$ versus $$O(\omega ^{-2})$$ for GS, $$O((2Q_s)^{(N+M)})$$ for ES, and $$O(\iota ^{-4})$$ for REINFORCE, which exhibits inference times on the order of milliseconds, compared to the computationally intractable costs associated with ES. These results show that the proposed algorithm for IRS-assisted partial D2D/MEC offloading is an effective and practical approach for jointly enhancing computing efficiency and latency in next-generation wireless systems.