  We study wireless power transmission by an energy source to multiple energy
harvesting nodes with the aim to maximize the energy efficiency. The source
transmits energy to the nodes using one of the available power levels in each
time slot and the nodes transmit information back to the energy source using
the harvested energy. The source does not have any channel state information
and it only knows whether a received codeword from a given node was
successfully decoded or not. With this limited information, the source has to
learn the optimal power level that maximizes the energy efficiency of the
network. We model the problem as a stochastic Multi-Armed Bandits problem and
develop an Upper Confidence Bound based algorithm, which learns the optimal
transmit power of the energy source that maximizes the energy efficiency.
Numerical results validate the performance guarantees of the proposed algorithm
and show significant gains compared to the benchmark schemes.
