Title: Batch Reinforcement Learning Through Continuation Method. Abstract: Many real-world applications of reinforcement learning (RL) require the agent to learn from a fixed set of trajectories, without collecting new interactions.  Policy optimization under this setting is extremely challenging as: 1) the geometry of the objective function is hard to optimize efficiently; 2) the shift of data distributions causes high noise in the value estimation. In this work, we propose a simple yet effective policy iteration approach to batch RL using global optimization techniques known as continuation.  By constraining the difference between the learned policy and the behavior policy that generates the fixed trajectories, and continuously relaxing the constraint, our method 1) helps the agent escape local optima; 2) reduces the error in policy evaluation in the optimization procedure.   We present results on a variety of control tasks, game environments, and a recommendation task to empirically demonstrate the efficacy of our proposed method.