  With the evolution of artificial intelligence-generated content (AIGC)
techniques and the development of space-air-ground integrated networks (SAGIN),
there will be a growing opportunity to enhance more users' mobile experience
with customized AIGC applications. This is made possible through the use of
parameter-efficient fine-tuning (PEFT) training alongside mobile edge
computing. In this paper, we formulate the optimization problem of maximizing
the parameter training efficiency of the SAGIN system over wireless networks
under limited resource constraints. We propose the Parameter training
efficiency Aware Resource Allocation (PARA) technique to jointly optimize user
association, data offloading, and communication and computational resource
allocation. Solid proofs are presented to solve this difficult sum of ratios
problem based on quadratically constrained quadratic programming (QCQP),
semidefinite programming (SDP), graph theory, and fractional programming (FP)
techniques. Our proposed PARA technique is effective in finding a stationary
point of this non-convex problem. The simulation results demonstrate that the
proposed PARA method outperforms other baselines.
