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

Persio, Luca Di; Garbelli, Matteo

doi:10.3390/sym13010014

Cited by 6 publications

(6 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many applications have been developed, such as the zoom meeting, Google meets, Microsoft teams, Skype, etc. [23]. All of these applications can accommodate hundreds of people at a time [24,25].…”

Section: Introductionmentioning

confidence: 99%

A Technology Acceptance Model-Based Analytics for Online Mobile Games Using Machine Learning Techniques

et al. 2021

View full text Add to dashboard Cite

In recent years, the enhancement in technology has been envisioning for people to complete tasks in an easier way. Every manufacturing industry requires heavy machinery to accomplish tasks in a symmetric and systematic way, which is much easier with the help of advancement in the technology. The technological advancement directly affects human life as a result. It is found that humans are now fully dependent on it. The online game industry is one example of technology breakthrough. It is now a prominent industry to develop online games at world level. In this paper, our main objective is to analyze major factors which encourage mobile games industry to expand. Analyzing the system and symmetric relations inside can be done into two phases. The first phase is through a TAM Model, which is a very efficient way to solve statistical problems, and the second phase is with machine learning (ML) techniques, such as SVM, logistic regression, etc. Both strategies are popular and efficient in analyzing a system while maintaining the symmetry in a better way. Therefore, according to results from both the TAM model and ML approach, it is clear that perceived usefulness, attitude, and symmetric flow are important factors for game industry. The analytics provide a clear insight that perceived usefulness is an important parameter over behavior intention for the online mobile game industry.

show abstract

Section: Introductionmentioning

confidence: 99%

A Technology Acceptance Model-Based Analytics for Online Mobile Games Using Machine Learning Techniques

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Following [9,10], the SL problem aims at estimating the function F : X → Y, commonly known as the Oracle. The space X can be identified with a subset of R d related to input arrays (such as images, string texts, or time series), while Y is the corresponding target set.…”

Section: The Supervised Learning Paradigmmentioning

confidence: 99%

“…Moreover, the training of the NN is based on the correspondence between the empirical measure of neurons µ N and the function f N that is approximated by the NN. Specifically, it has been proved that training via gradient descent of an over-parametrised one-hidden-layer NN with infinite width is equivalent to gradient flow in Wasserstein space [2,9,14,15]. Conversely, in the small learning rate regime, the training is equivalent to an SDE, see, e.g., [16].…”

Section: Empirical Risk Minimizationmentioning

confidence: 99%

See 1 more Smart Citation

From Optimal Control to Mean Field Optimal Transport via Stochastic Neural Networks

Di Persio,

Garbelli

2023

Symmetry

Self Cite

View full text Add to dashboard Cite

In this paper, we derive a unified perspective for Optimal Transport (OT) and Mean Field Control (MFC) theories to analyse the learning process for Neural Network algorithms in a high-dimensional framework. We consider a Mean Field Neural Network in the context of MFC theory referring to the mean field formulation of OT theory that may allow the development of efficient algorithms in a high-dimensional framework while providing a powerful tool in the context of explainable Artificial Intelligence.

show abstract

“…For this we require stochastic optimal control and especially mean-field type optimal control [11], and, in this paradigm, the solution to the optimal control problem satisfies a system of partial differential equations instead of ordinary differential equations. The idea of using stochastic optimal control for deep learning was studied in [27,88], however, the main difference is we use elimination theorem of [24] to reduce the system of partial differential equations to hydrodynamic equation with advected quantity.…”

Section: Stochastic Optimal Control For Deep Learningmentioning

confidence: 99%

Deep Learning: Hydrodynamics, and Lie-Poisson Hamilton-Jacobi Theory

Ganaba

2021

Preprint

View full text Add to dashboard Cite

The interpretation of deep learning as a dynamical system has gained a considerable attention in recent years as it provides a promising framework. It allows for the use of existing ideas from established fields of mathematics for studying deep neural networks. In this article we present deep learning as an equivalent hydrodynamics formulation which in fact possess a Lie-Poisson structure and this further allows for using Poisson geometry to study deep learning. This is possible by considering the training of a deep neural network as a stochastic optimal control problem, which is solved using mean-field type control. The optimality conditions for the stochastic optimal control problem yield a system of partial differential equations, which we reduce to a system of equations of quantum hydrodynamics. We further take the hydrodynamics equivalence to show that, with conditions imposed on the network, that it is equivalent to the nonlinear Schrödinger equation.As the such systems have a particular geometric structure, we also present a structure-preserving numerical scheme based on the Hamilton-Jacobi theory and its Lie-Poisson version known as Lie-Poisson Hamilton-Jacobi theory. The choice of this scheme was decided by the fact it can be applied to both deterministic and mean-field type control Hamiltonians. Not only this method eliminates the possibility of the emergence of fictitious solutions, it also eliminates the need for additional constraints when constructing high order methods.

show abstract

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

Cited by 6 publications

References 10 publications

A Technology Acceptance Model-Based Analytics for Online Mobile Games Using Machine Learning Techniques

A Technology Acceptance Model-Based Analytics for Online Mobile Games Using Machine Learning Techniques

From Optimal Control to Mean Field Optimal Transport via Stochastic Neural Networks

Deep Learning: Hydrodynamics, and Lie-Poisson Hamilton-Jacobi Theory

Contact Info

Product

Resources

About