The popular Q-learning algorithm is known to overestimate action values under certain conditions. It was not previously known whether, in practice, such overestimations are common, whether they harm performance, and whether they can generally be prevented. In this paper, we answer all these questions affirmatively. In particular, we first show that the recent DQN algorithm, which combines Q-learning with a deep neural network, suffers from substantial overestimations in some games in the Atari 2600 domain. We then show that the idea behind the Double Q-learning algorithm, which was introduced in a tabular setting, can be generalized to work with large-scale function approximation. We propose a specific adaptation to the DQN algorithm and show that the resulting algorithm not only reduces the observed overestimations, as hypothesized, but that this also leads to much better performance on several games. The goal of reinforcement learning (Sutton and Barto, 1998) is to learn good policies for sequential decision problems, by optimizing a cumulative future reward signal. Q-learning (Watkins, 1989 ) is one of the most popular reinforcement learning algorithms, but it is known to sometimes learn unrealistically high action values because it includes a maximization step over estimated action values, which tends to prefer overestimated to underestimated values. In previous work, overestimations have been attributed to insufficiently flexible function approximation (Thrun and Schwartz, 1993) and noise (van Hasselt, 2010 (van Hasselt, , 2011 . In this paper, we unify these views and show overestimations can occur when the action values are inaccurate, irrespective of the source of approximation error. Of course, imprecise value estimates are the norm during learning, which indicates that overestimations may be much more common than previously appreciated. It is an open question whether, if the overestimations do occur, this negatively affects performance in practice. Overoptimistic value estimates are not necessarily a problem in and of themselves. If all values would be uniformly higher then the relative action preferences are preserved and we would not expect the resulting policy to be any worse. Furthermore, it is known that sometimes it is good to be optimistic: optimism in the face of uncertainty is a well-known exploration technique (Kaelbling et al., 1996) . If, however, the overestimations are not uniform and not concentrated at states about which we wish to learn more, then they might negatively affect the quality of the resulting policy. Thrun and Schwartz (1993) give specific examples in which this leads to suboptimal policies, even asymptotically. To test whether overestimations occur in practice and at scale, we investigate the performance of the recent DQN algorithm . DQN combines Q-learning with a flexible deep neural network and was tested on a varied and large set of deterministic Atari 2600 games, reaching human-level performance on many games. In some ways, this setting is a best-case scenario for Q-learning, because the deep neural network provides flexible function approximation with the potential for a low asymptotic approximation error, and the determinism of the environments prevents the harmful effects of noise. Perhaps surprisingly, we show that even in this comparatively favorable setting DQN sometimes substantially overestimates the values of the actions. We show that the idea behind the Double Q-learning algorithm (van Hasselt, 2010) , which was first proposed in a tabular setting, can be generalized to work with arbitrary function approximation, including deep neural networks. We use this to construct a new algorithm we call Double DQN. We then show that this algorithm not only yields more accurate value estimates, but leads to much higher scores on several games. This demonstrates that the overestimations of DQN were indeed leading to poorer policies and that it is beneficial to reduce them. In addition, by improving upon DQN we obtain state-of-the-art results on the Atari domain.
One of these is the Double DQN introduced by REF .
Deep Reinforcement Learning with Double Q-learning
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Mathematics Computer Science