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.
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