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This study investigates the mean-variance (MV) trade-off in reinforcementlearning (RL), an instance of the sequential decision-making under uncertainty.Our objective is to obtain MV-efficient policies whose means and variances arelocated on the Pareto efficient frontier with respect to the MV trade-off;under the condition, any increase in the expected reward would necessitate acorresponding increase in variance, and vice versa. To this end, we propose amethod that trains our policy to maximize the expected quadratic utility,defined as a weighted sum of the first and second moments of the rewardsobtained through our policy. We subsequently demonstrate that the maximizerindeed qualifies as an MV-efficient policy. Previous studies that employedconstrained optimization to address the MV trade-off have encounteredcomputational challenges. However, our approach is more computationallyefficient as it eliminates the need for gradient estimation of variance, acontributing factor to the double sampling issue observed in existingmethodologies. Through experimentation, we validate the efficacy of ourapproach.

Mean-Variance Efficient Reinforcement Learning with Applications to Dynamic Financial Investment