Mitigating excessive vibration of civil engineering structures using various types of devices has been a conspicuous research topic in the past few decades. Some devices, such as electromagnetic transducers, which have a capability of exerting control forces while simultaneously harvesting energy, have been proposed recently. These devices make possible a self-regenerative system that can semi-actively mitigate structural vibration without the need of external energy. Integrating mechanical, electrical components, and control algorithms, these devices open up a new research domain that needs to be addressed. In this study, the feasibility of using an actor-critic based reinforcement learning control algorithm for simultaneous vibration control and energy harvesting for a civil engineering structure is investigated. The actor-critic based reinforcement learning control algorithm is a real-time, model-free adaptive technique that can adjust the controller parameters based on observations and reward signals without knowing the system characteristics. It is suitable for the control of a partially known nonlinear system with uncertain parameters. The feasibility of implementing this algorithm on a building structure equipped with an electromagnetic damper will be investigated in this study. Issues related to the modelling of learning algorithm, initialization and convergence will be presented and discussed.