Back-propagation is a popular machine learning algorithm that uses gradient descent in training neural networks for supervised learning, but can be very slow. A number of algorithms have been developed to speed up convergence and improve robustness of the learning. However, they are complicated to implement biologically as they require information from previous updates. Inspired by synaptic competition in biology, we have come up with a simple and local gradient descent optimization algorithm that can reduce training time, with no demand on past details. Our algorithm, named dynamic learning rate (DLR), works similarly to the traditional gradient descent used in back-propagation, except that instead of having a uniform learning rate across all synapses, the learning rate depends on the current neuronal connection weights. Our algorithm is found to speed up learning, particularly for small networks.