Much recent research activity has focused on the theory and application of quantum calculus. This branch of mathematics continues to find new and useful applications and there is much promise left for investigation into this field. We present a formulation of dynamic programming grounded in the quantum calculus. Our results include the standard dynamic programming induction algorithm which can be interpreted as the Hamilton-Jacobi-Bellman equation in the quantum calculus. Furthermore, we show that approximate dynamic programming in quantum calculus is tenable by laying the groundwork for the backpropagation algorithm common in neural network training. In particular, we prove that the chain rule for ordered derivatives, fundamental to backpropagation, is valid in quantum calculus. In doing this we have connected two major fields of research.
J. E. Seiffertt and D. C. Wunsch, "A Quantum Calculus Formulation of Dynamic Programming and Ordered Derivatives," Proceedings of the IEEE International Joint conference on Neural Networks, 2008. IJCNN 2008. (IEEE World Congress on Computational Intelligence), Institute of Electrical and Electronics Engineers (IEEE), Jun 2008.
The definitive version is available at https://doi.org/10.1109/IJCNN.2008.4634327
IEEE International Joint conference on Neural Networks, 2008. IJCNN 2008. (IEEE World Congress on Computational Intelligence)
Electrical and Computer Engineering
Keywords and Phrases
Backpropagation; Dynamic Equations; Dynamic Programming; Quantum Calculus; Time Scales
Article - Conference proceedings
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