Unexpected loads in Cloud data centers may trigger overloaded situation and performance degradation. To guarantee system performance, cloud computing environment is required to have the ability to handle overloads. The existing approaches, like Dynamic Voltage Frequency Scaling and VM consolidation, are effective in handling partial overloads, however, they cannot function when the whole data center is overloaded. Brownout has been proved to be a promising approach to relieve the overloads through deactivating application non-mandatory components or microservices temporarily. Moreover, brownout has been applied to reduce data center energy consumption. It shows that there are trade-offs between energy saving and discount offered to users (revenue loss) when one or more services are not provided temporarily. In this paper, we propose a brownout-based approximate Markov Decision Process approach to improve the aforementioned trade-offs. The results based on real trace demonstrate that our approach saves 20% energy consumption than VM consolidation approach. Compared with existing energy-efficient brownout approach, our approach reduces the discount amount given to users while saving similar energy consumption.