Backpropagation versus dynamic programming approach for neural networks learning

The learning of multi-layer neural networks can be considered as a special case of a multi-stage optimal control problem. In such a case, the layers are treated as stages and the weights as controls. The problem of optimal weight adjustment is converted into an optimal control problem. The multi-stage optimal control problem can be solved by the application of the dynamic programming method. Within the backpropagation framework, weights are tuned layer-by-layer, as well as step-by-step, in order to minimize the learning error. Meanwhile, within the new algorithm, for each layer, starting from the output layer, a return function is first constructed, and then this function must be minimized with respect to the weights. This procedure is done stage-by-stage (i.e. layer-by-layer)