Distributed Optimization-Learning with Graph Transformers for Terahertz Cell-Free Integrated Sensing and Communication Systems

In this paper, we propose a distributed optimization-learning framework for terahertz (THz) cell-free integrated sensing and communication (CF-ISAC) systems, termed Distributed Optimization-Learning with Graph Transformers (DOLG). We first formulate a highly non-convex joint scheduling and signal design problem for THz CF-ISAC systems, jointly optimizing access point (AP)-user equipment (UE) association and beamforming under signal to interference plus noise ratio based communication and Cramér-Rao bound based sensing constraints, together with line-of-sight-driven visibility rules and per-AP power constraints. We also develop an optimization based benchmark utilizing a tractable relaxed reformulation. Building upon this optimization structure, we redesign a graph transformer network (GTN) as an optimization-aware representation module that encodes cross-field wavefront geometry, blockage visibility, and sensing relevance in a permutation-equivariant manner. The proposed DOLG framework amortizes the iterative optimization procedure into a scalable GTN-conditioned distributed multi-agent reinforcement learning policy through centralized training and decentralized execution, while preserving per-AP power constraints via structure-preserving projections. Simulation results demonstrate that the proposed DOLG framework achieves stable convergence and effectively balances the communication-sensing tradeoff. From the system-level perspective, it outperforms multicell and non-joint design baselines. Furthermore, it surpasses conventional optimization based and heuristic approaches in terms of both ISAC performance and computational scalability.