The evolution of social robots has increased with the advent of recent artificial intelligence techniques. Alongside humans, social robots play active roles in various household and industrial applications. However, the safety of humans becomes a significant concern when robots navigate in a complex and crowded environment. In literature, the safety of humans in relation to social robots has been addressed by various methods; however, most of these methods compromise the time efficiency of the robot. For robots, safety and time-efficiency are two contrast elements where one dominates the other. To strike a balance between them, a multi-reward formulation in the reinforcement learning framework is proposed, which improves the safety together with time-efficiency of the robot. The multi-reward formulation includes both positive and negative rewards that encourage and punish the robot, respectively. The proposed reward formulation is tested on state-of-the-art methods of multi-agent navigation. In addition, an ablation study is performed to evaluate the importance of individual rewards. Experimental results signify that the proposed approach balances the safety and the time-efficiency of the robot while navigating in a crowded environment.