1. A system for pre-distorting a signal applied to a power amplifier to compensate for distortion introduced by the power amplifier at different power settings, comprising: a pre-distorter for pre-distorting the signal according to a pre-distortion polynomial, prior to amplification of the signal by the power amplifier; an adaptive estimator for adaptively estimating and applying pre-distortion polynomial coefficients to the pre-distorter, wherein the adaptive estimator includes a first estimation loop for saving successive iterations of the adaptive estimator; and a second estimation loop including an estimation regularizer for regularizing estimation of the pre-distortion polynomial coefficients over successive iterations according to a modified objective function that initially constrains growth in a magnitude of the pre-distortion polynomial coefficients and then relaxes the constraint in growth over successive iterations until an estimation is reduced to a steady-state least squares estimation.