Distributional Reinforcement Learning with Dual Expectile-Quantile Regression

Successful applications of distributional reinforcement learning with quantile regression prompt a natural question: can we use other statistics to represent the distribution of returns? In particular, expectile regression is known to be more efficient than quantile regression for approximating distributions, especially on extreme values, and by providing a straightforward estimator of the mean it is a natural candidate for reinforcement learning. Prior work has answered this question positively in the case of expectiles, with the major caveat that expensive computations must be performed to ensure convergence. In this work, we propose a dual expectile-quantile approach which solves the shortcomings of previous work while leveraging the complementary properties of expectiles and quantiles. Our method outperforms both quantile-based and expectile-based baselines on the MuJoCo continuous control benchmark.