Time-varying fast fading channels present a major challenge in the design of wireless communication systems. Pilot Symbol Assisted Modulation (PSAM) has been introduced to mitigate the effects of fading and allow coherent demodulation. Our work studies the performance of \emph{non-feedback} adaptive PSAM scheme over time-varying Rayleigh fading channels. A modular method is introduced for computing the rates in an efficient manner. Moreover, four transmission policies are analyzed and we show how optimal training in terms of duration and power allocation varies with the channel conditions and from one transmission policy to another. The performance of these schemes is measured in terms of achievable rates using binary signaling. We formally show that, for a causal estimation, placing all the power on the last pilot symbol is expected to be optimal. Furthermore, the autocorrelation of the fading process is based either on a stationary first order Gauss-Markov modeling of the process or on Jakes' model when higher orders of correlation are analyzed.