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Model-free deep reinforcement learning has achieved great success in many domains, such as video games, recommendation systems and robotic control tasks. In continuous control tasks, widely used policies with Gaussian distributions results in ineffective exploration of environments and limited performance of algorithms in many cases. In this paper, we propose a density-free off-policy algorithm, Generative Actor-Critic(GAC), using the push-forward model to increase the expressiveness of policies, which also includes an entropy-like technique, MMD-entropy regularizer, to balance the exploration and exploitation. Additionnally, we devise an adaptive mechanism to automatically scale this regularizer, which further improves the stability and robustness of GAC. The experiment results show that push-forward policies possess desirable features, such as multi-modality, which can improve the efficiency of exploration and asymptotic performance of algorithms obviously., Comment: This paper has something wrong