This article presents a novel neural network training approach for faster convergence and better generalization abilities in deep reinforcement learning (RL). Particularly, we focus on the enhancement of training and evaluation performance in RL algorithms by systematically reducing gradient's variance and, thereby, providing a more targeted learning process. The proposed method, which we term gradient monitoring (GM), is a method to steer the learning in the weight parameters of a neural network based on the dynamic development and feedback from the training process itself. We propose different variants of the GM method that we prove to increase the underlying performance of the model. One of the proposed variants, momentum with GM (M-WGM), allows for a continuous adjustment of the quantum of backpropagated gradients in the network based on certain learning parameters. We further enhance the method with the adaptive M-WGM (AM-WGM) method, which allows for automatic adjustment between focused learning of certain weights versus more dispersed learning depending on the feedback from the rewards collected. As a by-product, it also allows for automatic derivation of the required deep network sizes during training as the method automatically freezes trained weights. The method is applied to two discrete (real-world multirobot coordination problems and Atari games) and one continuous control task (MuJoCo) using advantage actor-critic (A2C) and proximal policy optimization (PPO), respectively. The results obtained particularly underline the applicability and performance improvements of the methods in terms of generalization capability.