Machine Learning architectures for price formation models

Gomes, Diogo A.; Gutiérrez, Julián; Laurière, Mathieu

doi:10.48550/arxiv.2204.03968

Cited by 3 publications

(3 citation statements)

References 20 publications

(35 reference statements)

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“…This technique was proposed in [56] (with a single neural network function of time and space instead of a sequence of neural networks functions of space online). Although we focus here on a basic setting for which a simple feedforward fully connected architecture performs well, other architectures may yield better results for problems with more complex time dependencies; see e.g., [90,100] for applications with RNNs. See also [94,7] and the survey [57] for more details.…”

Section: Mean-field Type Controlmentioning

confidence: 99%

Recent Developments in Machine Learning Methods for Stochastic Control and Games

Hu¹,

Laurière²

2023

Preprint

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In this paper, we give an overview of recently developed machine learning methods for stochastic control problems and games. The main focus is on deep learning methods that have unlocked the possibility to solve such problems even when the structure is complex or the dimension is high, which is not feasible with traditional numerical methods. The new approaches build on recent breakthrough machine learning methods for high-dimensional partial differential equations or backward stochastic differential equations, or on model-free reinforcement learning for Markov decision processes. This review summarizes state-of-the-art works at the crossroad of machine learning and stochastic control and games. It also discusses connections with real applications and identifies unsolved challenges.

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Section: Mean-field Type Controlmentioning

confidence: 99%

Recent Developments in Machine Learning Methods for Stochastic Control and Games

Hu¹,

Laurière²

2023

Preprint

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“…Note that this method was extended to the mean-field setting in [68,46,7]. Although we focus here on a basic setting for which a simple feedforward fully connected architecture performs well, other architectures may yield better results for problems with more complex time dependencies, see e.g., [68,77].…”

Section: Mean-field Type Controlmentioning

confidence: 99%

Recent Developments in Machine Learning Methods for Stochastic Control and Games

Laurière

2022

SSRN Journal

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“…Moreover, the recent progress on machine learning technologies made it easier to test and provide more efficient approximations of the solutions to complex mean-field type control problems. The link between deep learning and control/games problems was recently studied by a number of others in series of papers (see, e.g., [16][17][18][19][20][21][22][23]), where the authors (jointly and/or independently) proposed algorithms for the solution of mean-field optimal control problems based on approximations of the theoretical solutions by neural networks, using the software package TensorFlow with its "Stochastic Gradient Descent" optimizer designed for machine learning. However, to the best of our knowledge, the mean-field type game case and the related stability of the associated neural networks were not considered in the literature so far.…”

Section: Introductionmentioning

confidence: 99%

Data‐driven stability of stochastic mean‐field type games via noncooperative neural network adversarial training

Barreiro-Gómez

Choutri

2023

Asian Journal of Control

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We propose an approach to neural network stochastic differential games of mean‐field type and its corresponding stochastic stability analysis by means of adversarial training (aka adversarial attacks). This is a class of data‐driven differential games where the distribution of the variables such as the system states and the decision‐makers' strategies (control inputs) is incorporated into the problem. This work casts the cooperative/noncooperative game terminology into the deep learning framework where we talk about cooperative and noncooperative neural network computations that involve learning capabilities and neural network architectures. We suggest a method to computationally validate the feasibility of the approximated solutions via neural networks and evaluate the stochastic stability of the associated closed‐loop system (state feedback Nash). Moreover, we enhance the stochastic stability by enlarging the training set with adversarial initial states to obtain a more robust neural network for a particular decision‐maker. Finally, a worked‐out example based on the linear‐quadratic mean‐field type game (LQ‐MTG) that illustrates our methodology is presented.

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Machine Learning architectures for price formation models

Cited by 3 publications

References 20 publications

Recent Developments in Machine Learning Methods for Stochastic Control and Games

Recent Developments in Machine Learning Methods for Stochastic Control and Games

Recent Developments in Machine Learning Methods for Stochastic Control and Games

Data‐driven stability of stochastic mean‐field type games via noncooperative neural network adversarial training

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