Before revision:  The new method has two desired properties:1) it can flexibly adjust the bootstrap step based on the quality of the data and the learned value function; 2) it can safely and robustly utilize data from arbitrary behavior policy without additional correction, whatever its quality or "off-policyness". We analyze the theoretical properties of the related operator, showing that it is able to converge to the global optimal value function , with a ratio faster than the traditional Bellman Optimality Operator.
After revision:  The new method that bridges a highway that allows unimpeded information to flow across long horizons. The key to our method is a newly proposed Bellman equation, called Greedy-Step Bellman Optimality Equation, through which the high-credit information can fast propagate across a long horizon. We theoretically show that the solution of the new equation is exactly the optimal value function , with a ratio faster than the traditional Bellman Optimality Operator.