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This study investigates the mean-variance (MV) trade-off in reinforcement learning (RL), an instance of the sequential decision-making under uncertainty. Our objective is to obtain MV-efficient policies whose means and variances are located on the Pareto efficient frontier with respect to the MV trade-off; under the condition, any increase in the expected reward would necessitate a corresponding increase in variance, and vice versa. To this end, we propose a method that trains our policy to maximize the expected quadratic utility, defined as a weighted sum of the first and second moments of the rewards obtained through our policy. We subsequently demonstrate that the maximizer indeed qualifies as an MV-efficient policy. Previous studies that employed constrained optimization to address the MV trade-off have encountered computational challenges. However, our approach is more computationally efficient as it eliminates the need for gradient estimation of variance, a contributing factor to the double sampling issue observed in existing methodologies. Through experimentation, we validate the efficacy of our approach.