  The problem of Raman amplifier optimization is studied. A differentiable
interpolation function is obtained for the Raman gain coefficient using machine
learning (ML), which allows for the gradient descent optimization of
forward-propagating Raman pumps. Both the frequency and power of an arbitrary
number of pumps in a forward pumping configuration are then optimized for an
arbitrary data channel load and span length. The forward propagation model is
combined with an experimentally-trained ML model of a backward-pumping Raman
amplifier to jointly optimize the frequency and power of the forward
amplifier's pumps and the powers of the backward amplifier's pumps. The joint
forward and backward amplifier optimization is demonstrated for an unrepeatered
transmission of 250 km. A gain flatness of $<$ 1~dB over 4 THz is achieved. The
optimized amplifiers are validated using a numerical simulator.
