We present a real-time adaptive Digital PreDistortion (DPD) system developed on a System-on-Chip (SoC) platform with integrated RF front end, namely the AMD/Xilinx RFSoC. The design utilizes the heterogeneity of the RFSoC and is carefully partitioned. The control logic and training algorithm are implemented on the embedded ARM processor, while the predistorter module is placed on the FPGA fabric. To better coordinate both the hardware and software implementations, the training algorithm has been optimized for a shorter training time which results in a system that adapts to current environmental conditions with a shorter latency. Specifically, the number of signal samples used in training are reduced by applying the probability distribution information from the input signal in order to reduce the training time while retaining the important data samples. Results show that this reduced training set maintains the accuracy of the full data set. The implemented design balances the processing on the ARM processor and FPGA fabric resulting in a computationally efficient solution which makes good use of the different resources available. It has been experimentally validated on an AMD/Xilinx Gen3 RFSoC board with an exsternal GaN Power Amplifier (PA).