Abstract
We present optimal control approach to improve the neural network learned on a given empirical data (set of observations). Artificial neural networks usually are described as black-boxes and it is difficult to say something about their properties than very general results received from learning data. For many applications, e.g. medicine or embedded system for controlling autonomous vehicles, it is essential to say not only that on training data we get some error but that we will make an error not greater than some \(\varepsilon \) for every data we can input to our system. To derive required theory we apply an optimal control theory to a certain family of neutral networks, considered as ordinary differential equations, defined by a set of controls and suitable constructed functional.
Very often we have additional information or knowledge on the problem the data represent. Our approach allows to include these information and knowledge in the construction of the model.
We apply a modification of classical dynamic programming ideas to formulate a new optimization problem. We use it to state and prove sufficient approximate optimality conditions for finding approximate neural network which should work correctly for given \(\varepsilon \) with respect to built functional, on a data different than the set of observations.
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Lipnicka, M., Nowakowski, A. (2022). Optimal Control in Learning Neural Network. In: Le Thi, H.A., Pham Dinh, T., Le, H.M. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. MCO 2021. Lecture Notes in Networks and Systems, vol 363. Springer, Cham. https://doi.org/10.1007/978-3-030-92666-3_26
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DOI: https://doi.org/10.1007/978-3-030-92666-3_26
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