Large number of antennas and radio frequency (RF) chains at the base stations (BSs) lead to high energy consumption in massive MIMO systems. Thus, how to improve the energy efficiency (EE) with a computationally efficient approach is a significant challenge in the design of massive MIMO systems. With this motivation, a learning-based stochastic gradient descent algorithm is proposed in this paper to obtain the optimal joint uplink and downlink EE with joint antenna selection and user scheduling in single-cell massive MIMO systems. Using Jensen's inequality and the characteristics of wireless channels, a lower bound on the system throughput is obtained. Subsequently, incorporating the power consumption model, the corresponding lower bound on the EE of the system is identified. Finally, learning-based stochastic gradient descent method is used to solve the joint antenna selection and user scheduling problem, which is a combinatorial optimization problem. Rare event simulation is embedded in the learning-based stochastic gradient descent method to generate samples with very small probabilities. In the analysis, both perfect and imperfect channel side information (CSI) at the BS are considered. Minimum mean-square error (MMSE) channel estimation is employed in the study of the imperfect CSI case. In addition, the effect of a constraint on the number of available RF chains in massive MIMO system is investigated considering both perfect and imperfect CSI at the BS.