This paper leverages a classic prediction technique, known as parametric overlapped block motion compensation (POBMC), in a reinforcement learning framework for video prediction. Learning-based prediction methods with explicit motion models often suffer from having to estimate large numbers of motion parameters with artificial regularization. Inspired by the success of sparse motion-based prediction for video compression, we propose a parametric video prediction on a sparse motion field composed of few critical pixels and their motion vectors. The prediction is achieved by gradually refining the estimate of a future frame in iterative, discrete steps. Along the way, the identification of critical pixels and their motion estimation are addressed by two neural networks trained under a reinforcement learning setting. Our model achieves the state-of-the-art performance on CaltchPed, UCF101 and CIF datasets in one-step and multi-step prediction tests. It shows good generalization results and is able to learn well on small training data.