We provide a rigorous mathematical formulation of Deep Learning (DL) methodologies through an in-depth analysis of the learning procedures characterizing Neural Network (NN) models within the theoretical frameworks of Stochastic Optimal Control (SOC) and Mean-Field Games (MFGs). In particular, we show how the supervised learning approach can be translated in terms of a (stochastic) mean-field optimal control problem by applying the Hamilton–Jacobi–Bellman (HJB) approach and the mean-field Pontryagin maximum principle. Our contribution sheds new light on a possible theoretical connection between mean-field problems and DL, melting heterogeneous approaches and reporting the state-of-the-art within such fields to show how the latter different perspectives can be indeed fruitfully unified.

Deep Learning and Mean-Field Games: A Stochastic Optimal Control Perspective / Persio, Luca Di; Garbelli, Matteo. - In: SYMMETRY. - ISSN 2073-8994. - 13:1(2021), pp. 14.1-14.20. [10.3390/sym13010014]

Deep Learning and Mean-Field Games: A Stochastic Optimal Control Perspective

Persio, Luca Di;Garbelli, Matteo
2021

Abstract

We provide a rigorous mathematical formulation of Deep Learning (DL) methodologies through an in-depth analysis of the learning procedures characterizing Neural Network (NN) models within the theoretical frameworks of Stochastic Optimal Control (SOC) and Mean-Field Games (MFGs). In particular, we show how the supervised learning approach can be translated in terms of a (stochastic) mean-field optimal control problem by applying the Hamilton–Jacobi–Bellman (HJB) approach and the mean-field Pontryagin maximum principle. Our contribution sheds new light on a possible theoretical connection between mean-field problems and DL, melting heterogeneous approaches and reporting the state-of-the-art within such fields to show how the latter different perspectives can be indeed fruitfully unified.
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Persio, Luca Di; Garbelli, Matteo
Deep Learning and Mean-Field Games: A Stochastic Optimal Control Perspective / Persio, Luca Di; Garbelli, Matteo. - In: SYMMETRY. - ISSN 2073-8994. - 13:1(2021), pp. 14.1-14.20. [10.3390/sym13010014]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/296513
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