SEAL-MAC: Symmetry-Equivariant Lyapunov Actor–Critic for Queue-Stable MEC Offloading

Mobile edge computing (MEC) must serve rapidly growing populations of latency-critical and energy-constrained devices, yet distributed offloading faces two coupled problems: learned multi-agent policies depend on the arbitrary numerical ordering of edge servers, which wastes training samples and treats physically equivalent configurations inconsistently, while short-horizon cost minimization overloads attractive servers and destabilizes their queues. This paper presents SEAL-MAC (Symmetry-Equivariant Lyapunov Multi-Agent Actor–Critic), a distributed learning framework that addresses both problems jointly. First, a symmetric resource-set actor with a mirror consistency regularizer enforces server relabeling equivariance of each user’s policy and invariance of its value and Lyapunov critics. Second, a load-symmetric Lyapunov–potential shaping mechanism augments drift-plus-penalty rewards with normalized load-balance signals, coupling queue stability, fairness, and strategic alignment. The shaped interaction is analyzed as a Lyapunov-shaped Markov potential game: exact under orthogonal congestion-separable conditions, and a Markov α-potential game under heterogeneity or interference, yielding conditional finite-time (ϵ+α)-Nash convergence and mean-square queue stability. Each device learns from local observations and O(M) queue broadcasts without exchanging gradients or policies. In simulations with up to 200 users, SEAL-MAC reduces average delay by 9.0%, 95th-percentile delay by 11.8%, energy consumption by 10.6%, and the deadline-violation rate from 3.1% to 1.8% relative to the strongest Lyapunov baseline, halves the empirical one-step deviation gain of an identically shaped Ly-PPO agent (0.048 versus 0.098), and raises the Jain fairness index from 0.88 to 0.94.