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EMaQ: Expected-Max Q-Learning Operator for Simple Yet Effective Offline and Online RL

Seyed Kamyar Seyed Ghasemipour · Dale Schuurmans · Shixiang Gu


Off-policy reinforcement learning (RL) holds the promise of sample-efficient learning of decision-making policies by leveraging past experience. However, in the offline RL setting -- where a fixed collection of interactions are provided and no further interactions are allowed -- it has been shown that standard off-policy RL methods can significantly underperform. In this work, we closely investigate an important simplification of BCQ (Fujimoto et al., 2018) -- a prior approach for offline RL -- removing a heuristic design choice. Importantly, in contrast to their original theoretical considerations, we derive this simplified algorithm through the introduction of a novel backup operator, Expected-Max Q-Learning (EMaQ), which is more closely related to the resulting practical algorithm. Specifically, in addition to the distribution support, EMaQ explicitly considers the number of samples and the proposal distribution, allowing us to derive new sub-optimality bounds. In the offline RL setting -- the main focus of this work -- EMaQ matches and outperforms prior state-of-the-art in the D4RL benchmarks (Fu et al., 2020). In the online RL setting, we demonstrate that EMaQ is competitive with Soft Actor Critic (SAC). The key contributions of our empirical findings are demonstrating the importance of careful generative model design for estimating behavior policies, and an intuitive notion of complexity for offline RL problems. With its simple interpretation and fewer moving parts, such as no explicit function approximator representing the policy, EMaQ serves as a strong yet easy to implement baseline for future work.

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