  In this paper, we design a deep learning based resource allocation framework,
in the form of an auction, for simultaneous information and power transfer from
a hybrid access point (AP) to information devices and energy harvesting
devices, respectively. Using Myerson's lemma and the concept of virtual welfare
maximization, we develop an optimal dominant-strategy incentive-compatible
mechanism for the AP to maximize its expected revenue, based on the devices'
bid profiles, valuation distributions, demand profiles, and channel state
information. In so doing, we formulate the revenue maximization problem, which
is a mixed-integer non-linear program, and propose an efficient
Branch-and-Bound (BnB) algorithm to solve the problem using semidefinite
relaxation technique in each branch. Since the problem has exponential time
complexity, using BnB algorithms can be impractical for real-time applications.
To circumvent this, a deep neural network (DNN) is proposed, and trained to
predict the optimal mechanism for beamforming the data and the energy towards
the information and energy devices, respectively. We use the BnB algorithm to
solve the problem offline and populate the training dataset. The proposed DNN
architecture is indeed a multi-layer perceptron, which is trained well to map
the heterogeneous input to the desired output with high accuracy. Furthermore,
we propose a heuristic iterative solution whose accuracy performance is
comparable to that of the DNN-based solution. The heuristic solution has
polynomial time complexity whereas the DNN-based solution has linear time
complexity.
