  This paper investigates the joint data and pilot power optimization for
maximum sum spectral efficiency (SE) in multi-cell Massive MIMO systems, which
is a non-convex problem. We first propose a new optimization algorithm,
inspired by the weighted minimum mean square error (MMSE) approach, to obtain a
stationary point in polynomial time. We then use this algorithm together with
deep learning to train a convolutional neural network to perform the joint data
and pilot power control in sub-millisecond runtime, making it suitable for
online optimization in real multi-cell Massive MIMO systems. The numerical
result demonstrates that the solution obtained by the neural network is $1\%$
less than the stationary point for four-cell systems, while the sum SE loss is
$2\%$ in a nine-cell system.
