The step size is a parameter of fundamental importance in learning algorithms, particularly for the natural policy gradient (NPG) methods. We derive an upper bound for the step size in an incremental NPG estimation, and propose an adaptive step size to implement the derived upper bound. The proposed adaptive step size guarantees that an updated parameter does not overshoot the target, which is achieved by weighting the learning samples according to their relative importances. We also provide tight upper and lower bounds for the step size, though they are not suitable for the incremental learning. We confirm the usefulness of the proposed step size using the classical benchmarks. To the best of our knowledge, this is the first adaptive step size method for NPG estimation.

We propose a new closed-loop power control scheme for wireless mobile communication systems using an adaptive step size. The proposed scheme selects the basic power control step size by considering the speed of the mobile station and a variable step size by using instantaneous companding logic based on power control command bit patterns. We show its improved performance in view of the standard deviation of received power at the base station in consideration of channel BER.