  In most applications of utilizing neural networks for mathematical
optimization, a dedicated model is trained for each specific optimization
objective. However, in many scenarios, several distinct yet correlated
objectives or tasks often need to be optimized on the same set of problem
inputs. Instead of independently training a different neural network for each
problem separately, it would be more efficient to exploit the correlations
between these objectives and to train multiple neural network models with
shared model parameters and feature representations. To achieve this, this
paper first establishes the concept of common information: the shared knowledge
required for solving the correlated tasks, then proposes a novel approach for
model training by adding into the model an additional reconstruction stage
associated with a new reconstruction loss. This loss is for reconstructing the
common information starting from a selected hidden layer in the model. The
proposed approach encourages the learned features to be general and
transferable, and therefore can be readily used for efficient transfer
learning. For numerical simulations, three applications are studied: transfer
learning on classifying MNIST handwritten digits, the device-to-device wireless
network power allocation, and the multiple-input-single-output network downlink
beamforming and localization. Simulation results suggest that the proposed
approach is highly efficient in data and model complexity, is resilient to
over-fitting, and has competitive performances.
