Title: Faster Reinforcement Learning with Value Target Lower Bounding. Abstract: We show that an arbitrary lower bound of the maximum achievable value can be used to improve the Bellman value target during value learning.  In the tabular case, value learning using the lower bounded Bellman operator converges to the same optimal value as using the original Bellman operator, at a potentially faster speed.  In practice, discounted episodic return in episodic tasks and n-step bootstrapped return in continuing tasks can serve as lower bounds to improve the value target.  We experiment on Atari games, FetchEnv tasks and a challenging physically simulated car push and reach task.  We see large gains in sample efficiency as well as converged performance over common baselines such as TD3, SAC and Hindsight Experience Replay (HER) in most tasks, and observe a reliable and competitive performance against the stronger n-step methods such as td-lambda, Retrace and optimality tightening.  Prior works have already successfully applied a special case of lower bounding (using episodic return), but are limited to a small number of episodic tasks.  To the best of our knowledge, we are the first to propose the general method of value target lower bounding (with possibly bootstrapped return), to demonstrate its optimality in theory, and effectiveness in a wide range of tasks over many strong baselines.