Title: Revisiting Prioritized Experience Replay: A Value Perspective. Abstract: Reinforcement learning (RL) agents need to learn from past experiences. Prioritized experience replay that weighs experiences by their surprise (the magnitude of the temporal-difference error) significantly improves the learning efficiency for RL algorithms. Intuitively, surprise quantifies the unexpectedness of an experience to the learning agent. But how surprise is related to the importance of experience is not well understood. To address this problem, we derive three value metrics to quantify the importance of experience, which consider the extra reward would be earned by accessing the experience. We theoretically show these value metrics are upper-bounded by surprise for Q-learning. Furthermore, we successfully extend our theoretical framework to maximum-entropy RL by deriving the lower and upper bounds of these value metrics for soft Q-learning, which is also related to surprise. Our framework links two important quantities in RL, i.e., surprise and value of experience, and provides a theoretical basis to estimate the value of experience by surprise. We empirically show that the upper bounds hold in practice, and experience replay using the upper bound as priority improves maximum-entropy RL in Atari games. 