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Artificial intelligence is steadily increasing its impact on everyday life. Therefore, the societal issues of artificial intelligence have become an important concern in the AI research. The presence of data that reflects human biases towards historically discriminated groups defined by sensitive features such as race and gender, results in machine learning models which discriminate against these groups. In order to tackle the impact of bias in data, researchers developed a variety of specialized machine learning algorithms which are able to satisfy different fairness constraints imposed on the model. Group fairness constraints do not fit standard machine learning formulations easily due to their non-differentiable nature. In this paper we developed a technique for learning a fair classifier by Monte Carlo policy gradient method which naturally deals with such non-differentiable constraints. Our methodology focuses on direct optimization of both group fairness metric and predictive performance of the model. In addition, we propose two different variance reduction techniques of gradient estimation. We compare our models to seven other related and state-of-the-art models and demonstrate that they are able to achieve better trade-off between accuracy and unfairness. To the best of our knowledge, this is the first fair classification algorithm which solves the issue of non-differentiable constraints by reinforcement learning techniques. [ABSTRACT FROM AUTHOR]