Grey-Box Bayesian Optimization for ISAC in Fluid-Antenna Assisted Air-Ground Network
Fluid antenna systems (FAS) provide additional spatial diversity for integrated sensing and communication (ISAC) through joint port selection and precoding. \rev{However, existing designs commonly assume readily available channel state information, neglect residual self-interference, and combine communication and sensing into a single weighted objective. The resulting channel acquisition overhead, unmodeled residual self-interference, and limited characterization of the Pareto trade-off are critical obstacles to implementing ISAC in fluid-antenna-assisted air-ground networks.} \rev{To address these issues, we first formulate the joint design as a grey-box multi-objective optimization problem. This formulation retains the available analytical system mapping while treating the configuration-dependent channel and interference constituents as unknown, and directly represents the communication-sensing Pareto trade-off without predefined scalarization.} We then propose a tailored grey-box multi-objective Bayesian optimization (G-MOBO) method to solve the resulting high-dimensional problem. Specifically, G-MOBO learns the unknown constituents from performance feedback, propagates their predictive distributions through the known mapping, employs expected hypervolume improvement (EHI) to explore the Pareto frontier, and uses an adaptive trust region (TR) to localize the search. A temporal adaptation strategy is further incorporated to track the drifting Pareto frontier in time-varying environments. \rev{The theoretical analysis characterizes the sample efficiency of grey-box modeling and localized TR design via cumulative hypervolume regret.} Simulations demonstrate faster convergence, improved Pareto-frontier quality, and robust dynamic tracking compared with the considered baselines.