optimal control
A branch of mathematics for computing control policies that minimize a cost over time, the framework within which early backpropagation was formulated.
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Backpropagation Described by Arthur E. Bryson Jr. and Yu-Chi Ho
In 1969, Arthur E. Bryson Jr. and Yu-Chi Ho of Harvard University described a gradient-based optimisation procedure for multi-stage dynamic systems in their textbook Applied Optimal Control, presenting what is now recognised as an early statement of the backpropagation principle in a supervised-learning context.