This article presents a data-efficient learning approach for the complex-conjugate control of a wave energy point absorber. Particularly, the Bayesian Optimization algorithm is adopted for maximizing the extracted energy from sea waves subject to physical constraints. The algorithm learns the optimal coefficients of the causal controller. The simulation model of a Wavestar Wave Energy Converter (WEC) is selected to validate the control strategy for both the regular and irregular waves. The results indicate the efficiency and feasibility of the proposed control system. Less than 20 function evaluations are required to converge towards the optimal performance of each sea state. Additionally, this model-free controller can adapt to variations in the real sea state and be insensitive and robust to the WEC modeling bias.