Extreme Q-Learning: MaxEnt RL without Entropy

Modern Deep Reinforcement Learning (RL) algorithms require estimates of the maximal Q-value, which are difficult to compute in continuous domains with an infinite number of possible actions. In this work, we introduce a new update rule for online and offline RL which directly models the maximal value using Extreme Value Theory (EVT) inspired by Economics. By doing so, we avoid computing Q-values using out-of-distribution actions which is often a substantial source of error. Our key insight is to introduce an objective that directly estimates the optimal soft-value functions (LogSumExp) in the maximum entropy (MaxEnt) RL setting without needing to sample from a policy. Using EVT, we derive our \emph{Extreme Q-Learning} framework and consequently online and, for the first time, offline MaxEnt Q-learning algorithms, that do not explicitly require access to a policy or its entropy. Finally, our method obtains strong results in the Offline D4RL benchmark outperforming prior works by 10-20 points on some tasks while offering moderate improvements over SAC and TD3 on online DM Control tasks.