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With the increasing popularity of electric vehicles, distributed energy generation and storage facilities in smart grid systems, an efficient Demand-Side Management (DSM) is urgent for energy savings and peak loads reduction. Traditional DSM works focusing on optimizing the energy activities for a single household can not scale up to large-scale home energy management problems. Multi-agent Deep Reinforcement Learning (MA-DRL) shows a potential way to solve the problem of scalability, where modern homes interact together to reduce energy consumers consumption while striking a balance between energy cost and peak loads reduction. However, it is difficult to solve such an environment with the non-stationarity, and existing MA-DRL approaches cannot effectively give incentives for expected group behavior. In this paper, we propose a collective MA-DRL algorithm with continuous action space to provide fine-grained control on a large scale microgrid. To mitigate the non-stationarity of the microgrid environment, a novel predictive model is proposed to measure the collective market behavior. Besides, a collective behavior entropy is introduced to reduce the high peak loads incurred by the collective behaviors of all householders in the smart grid. Empirical results show that our approach significantly outperforms the state-of-the-art methods regarding power cost reduction and daily peak loads optimization.