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The recently proposed distributional approach to reinforcement learning(DiRL) is centered on learning the distribution of the reward-to-go, oftenreferred to as the value distribution. In this work, we show that thedistributional Bellman equation, which drives DiRL methods, is equivalent to agenerative adversarial network (GAN) model. In this formulation, DiRL can beseen as learning a deep generative model of the value distribution, driven bythe discrepancy between the distribution of the current value, and thedistribution of the sum of current reward and next value. We use this insightto propose a GAN-based approach to DiRL, which leverages the strengths of GANsin learning distributions of high-dimensional data. In particular, we show thatour GAN approach can be used for DiRL with multivariate rewards, an importantsetting which cannot be tackled with prior methods. The multivariate settingalso allows us to unify learning the distribution of values and statetransitions, and we exploit this idea to devise a novel exploration method thatis driven by the discrepancy in estimating both values and states.

Distributional Multivariate Policy Evaluation and Exploration with the Bellman GAN