In unmanned aerial vehicle ( UAV )-assisted networks, UAV acts as an aerial base station to serve ground users ( GUs ) through an access network, and meanwhile, the requested data traffic is acquired through the backhaul link. In this paper, we investigate an energy minimization problem with limited power supply for both backhaul and access links. The difficulties for solving such a non-convex and combinatorial problem lie at the high computational complexity/time. In solution development, we consider the approaches from both actor-critic deep reinforcement learning (AC- DRL ) and optimization perspectives. Firstly, two offline non-learning algorithms, i.e., an optimal and a heuristic algorithms, based on piecewise linear approximation and relaxation are developed as benchmarks. Secondly, towards real-time decision making, we improve the conventional AC- DRL and propose two learning schemes: AC-based user group scheduling and backhaul power allocation ( ACGP ), and joint AC-based user group scheduling and optimization-based backhaul power allocation ( ACGOP ). Numerical results show that the computation time of both ACGP and ACGOP are reduced tenfold to hundredfold compared to the offline approaches, where ACGOP is better than ACGP in energy savings. The results also verify the superiority of proposed learning solutions in terms of guaranteeing the feasibility and minimizing the system energy compared to the conventional AC- DRL .