Energy efficiency (EE) is one of the most important metrics for envisioned 6G networks, and sleep control, as a cost-efficient approach, can significantly lower power consumption by switching off network devices selectively. Meanwhile, the reconfigurable intelligent surface (RIS) has emerged as a promising technique to enhance the EE of future wireless networks. In this work, we jointly consider sleep and transmission power control for RIS-aided energy-efficient networks. In particular, considering the timescale difference between sleep control and power control, we introduce a cooperative hierarchical deep reinforcement learning (Co-HDRL) algorithm, enabling hierarchical and intelligent decision-making. Specifically, the meta-controller in Co-HDRL uses cross-entropy metrics to evaluate the policy stability of sub-controllers, and sub-controllers apply the correlated equilibrium to select optimal joint actions. Compared with conventional HDRL, Co-HDRL enables more stable high-level policy generations and low-level action selections. Then, we introduce a fractional programming method for RIS phase-shift control, maximizing the sum-rate under a given transmission power. In addition, we proposed a low-complexity surrogate optimization method as a baseline for RIS control. Finally, simulations show that the RIS-assisted sleep control can achieve more than 16\% lower energy consumption and 30\% higher EE than baseline algorithms.
