To Discount or Not to Discount in Reinforcement Learning: A Case Study Comparing R Learning and Q Learning

Most work in reinforcement learning (RL) is based on discounted techniques, such as Q learning, where long-term rewards are geometrically attenuated based on the delay in their occurence. Schwartz recently proposed an undiscounted RL technique called R learning that optimizes average reward, and argued that it was a better metric than the discounted one optimized by Q learning. In this paper we compare R learning with Q learning on a simulated robot box-pushing task. We compare these two techniques across three diierent exploration strategies: two of them undirected, Boltz-mann and semi-uniform, and one recency-based directed strategy. Our results show that Q learning performs better than R learning , even when both are evaluated using the same undiscounted performance measure. Furthermore, R learning appears to be very sensitive to choice of exploration strategy. In particular, a surprising result is that R learn-ing's performance noticeably deteriorates under Boltzmann exploration. We identify precisely a limit cycle situation that causes R learning's performance to deteriorate when combined with Boltzmann exploration, and show where such limit cycles arise in our robot task. However, R learning performs much better (although not as well as Q learning) when combined with semi-uniform and recency-based exploration. In this paper, we also argue for using medians over means as a better distribution-free estimator of average performance, and describe a simple non-parametric signiicance test for comparing learning data from two RL techniques.