For many of the reinforcement learning applications, the system is assumed to be inherently stable and with bounded reward, state and action space. These are key requirements for the optimization convergence of classical reinforcement learning reward function with discount factors. Unfortunately, these assumptions do not hold true for many real world problems such as an unstable linear–quadratic regulator (LQR). In this work, we propose new methods to stabilize and speed up the convergence of unstable reinforcement learning problems with the policy gradient methods. We provide theoretical insights on the efficiency of our methods. In practice, we achieve good experimental results over multiple examples where the vanilla methods mostly fail to converge due to system instability.