Artificial neural networks having competitive reward modulated spike time dependent plasticity and methods of training the same

A method of training an artificial neural network having a series of layers and at least one weight matrix encoding connection weights between neurons in successive layers. The method includes receiving, at an input layer of the series of layers, at least one input, generating, at an output layer of the series of layers, at least one output based on the at least one input, generating a reward based on a comparison of between the at least one output and a desired output, and modifying the connection weights based on the reward. Modifying the connection weights includes maintaining a sum of synaptic input weights to each neuron to be substantially constant and maintaining a sum of synaptic output weights from each neuron to be substantially constant.