A point-to-point wireless communication system in which the transmitter is
equipped with an energy harvesting device and a rechargeable battery, is
studied. Both the energy and the data arrivals at the transmitter are modeled
as Markov processes. Delay-limited communication is considered assuming that
the underlying channel is block fading with memory, and the instantaneous
channel state information is available at both the transmitter and the
receiver. The expected total transmitted data during the transmitter's
activation time is maximized under three different sets of assumptions
regarding the information available at the transmitter about the underlying
stochastic processes. A learning theoretic approach is introduced, which does
not assume any a priori information on the Markov processes governing the
communication system. In addition, online and offline optimization problems are
studied for the same setting. Full statistical knowledge and causal information
on the realizations of the underlying stochastic processes are assumed in the
online optimization problem, while the offline optimization problem assumes
non-causal knowledge of the realizations in advance. Comparing the optimal
solutions in all three frameworks, the performance loss due to the lack of the
transmitter's information regarding the behaviors of the underlying Markov
processes is quantified.