NG-SAC-M: Nash-guided SAC with migration for IoT healthcare

The growing deployment of IoT devices in healthcare telemonitoring requires computation offloading strategies that are energy-efficient, latency-aware, and theoretically grounded. Game-theoretic approaches provide Nash equilibrium guarantees but rely on static parameters; deep reinforcement learning (DRL) learns adaptive policies but lacks convergence guarantees. We propose NG-SAC-M (Nash-Guided Soft Actor-Critic with Migration), a framework that fuses congestion game theory with Soft Actor-Critic (SAC) DRL within a single optimization loop. The Critic is augmented with the Nash potential and regularized toward equilibrium allocations. A jointly-trained migration network learns when to trigger mobile agent migration for service continuity. Validated on three PhysioNet databases (16,723 clinical records, 8 pathological conditions), experiments over 30 independent runs show 43.3% energy reduction over no-offloading baselines and 23.9% over congestion game methods, with 70% lower latency variance through adaptive migration. Under a realistic 8-hour shift scenario with 20%/h battery drain, NG-SAC-M achieves 72.8% Message Delivery Rate, the highest among methods with Nash equilibrium guarantees (+76% over the congestion game baseline), while maintaining service continuity through proactive migration (SCR ≈ 100%). Under mass casualty conditions, NG-SAC-M maintains stable MDR across all emergency scenarios while providing Nash equilibrium existence guarantees and service continuity that pure DRL cannot offer.