We consider data transmission through a time-selective (correlated) 
flat Rayleigh fading channel under an average power constraint. The 
channel is estimated at the receiver with a pilot signal, and the 
estimate is fed back to the transmitter.  The estimate is used for 
coherent demodulation, and to adapt the data and pilot powers. Namely, 
the transmitter can conserve power by decreasing the training power when the
channel is faded. However, the channel estimate must always be sufficiently 
accurate to guide this adaptation.  By taking a continuous limit in which 
the channel becomes a diffusion (Ornstein-Uhlenbeck) process, which is 
estimated with a Kalman filter, we are able to solve for the optimal
training policy. Specifically, the optimal pilot power control
is "bang-bang", i.e., depending on the current system state (channel
estimate and associated error variance) the pilot power is either
the maximum allowable, or zero. The associated regions of the
state space are explicitly determined as a solution to a free boundary
partial differential equation. Numerical results show a significant 
increase in achievable rate due to the adaptive training scheme 
with feedback, relative to constant training, which does not require feedback.