  Radio on Free Space Optics (RoFSO), as a universal platform for heterogeneous
wireless services, is able to transmit multiple radio frequency signals at high
rates in free space optical networks. This paper investigates the optimal
design of power allocation for Wavelength Division Multiplexing (WDM)
transmission in RoFSO systems. The proposed problem is a weighted total
capacity maximization problem with two constraints of total power limitation
and eye safety concern. The model-based Stochastic Dual Gradient algorithm is
presented first, which solves the problem exactly by exploiting the null
duality gap. The model-free Primal-Dual Deep Learning algorithm is then
developed to learn and optimize the power allocation policy with Deep Neural
Network (DNN) parametrization, which can be utilized without any knowledge of
system models. Numerical simulations are performed to exhibit significant
performance of our algorithms compared to the average equal power allocation.
