Title: Optimistic Exploration with Backward Bootstrapped Bonus for Deep Reinforcement Learning. Abstract: Optimism in the face of uncertainty is a principled approach for provably efficient exploration for reinforcement learning in tabular and linear settings. However, such an approach is challenging in developing practical exploration algorithms for Deep Reinforcement Learning (DRL). To address this problem, we propose an Optimistic Exploration algorithm with Backward Bootstrapped Bonus (OEB3) for DRL by following these two principles. OEB3 is built on bootstrapped deep $Q$-learning, a non-parametric posterior sampling method for temporally-extended exploration. Based on such a temporally-extended exploration, we construct an UCB-bonus indicating the uncertainty of $Q$-functions. The UCB-bonus is further utilized to estimate an optimistic $Q$-value, which encourages the agent to explore the scarcely visited states and actions to reduce uncertainty. In the estimation of $Q$-function, we adopt an episodic backward update strategy to propagate the future uncertainty to the estimated $Q$-function consistently. Extensive evaluations show that OEB3 outperforms several state-of-the-art exploration approaches in Mnist maze and 49 Atari games.