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A mean field game inverse problem.
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This paper proposes mean-field game inverse-problem models to reconstruct the ground metrics and interaction kernels in the running costs, and numerically demonstrates that the model is both efficient and robust to noise.Abstract:
Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics and running costs of the games are of essential importance but are often unknown or only partially known. In this paper, we propose mean-field game inverse-problem models to reconstruct the ground metrics and interaction kernels in the running costs. The observations are the macro motions, to be specific, the density distribution, and the velocity field of the agents. They can be corrupted by noise to some extent. Our models are PDE constrained optimization problems, which are solvable by first-order primal-dual methods. Besides, we apply Bregman iterations to find the optimal model parameters. We numerically demonstrate that our model is both efficient and robust to noise.read more
Citations
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On an inverse boundary problem for mean field games
Hongyu Liu,Shengli Zhang +1 more
TL;DR: In this paper , the running cost function within any given proper (state) space-time subdomain is uniquely determined by the MFG boundary data of this subdomain, and a novel unique identifiability result is established by showing that the running costs within any proper subdomain are uniquely determined.
Journal ArticleDOI
Inverse problems for mean field games
TL;DR: In this paper , the authors studied the problem of recovering the running and terminal costs of mean field games with the Lagrangians of the players. And they showed that one can recover either the running cost or the terminal cost from knowledge of the total cost.
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A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problem
TL;DR: In this article , the inverse problem in mean-field games (MFGs) is considered and a fast and robust operator splitting algorithm is developed to solve the optimization using techniques including harmonic extensions, three-operator splitting scheme, and primal-dual hybrid gradient method.
Proceedings ArticleDOI
Riemannian Metric Learning via Optimal Transport
TL;DR: An optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold is introduced and it is shown that metrics learned using this method improve the quality of trajectory inference on scRNA and bird migration data at the cost of little additional cross-sections.
A Coefficient Inverse Problem for the Mean Field Games System
TL;DR: In this article , a Coefficient Inverse Problem (CIP) of the determination of a coefficient of the mean field games system of the second order is considered, where the input data are generated by a single measurement event.
References
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Journal ArticleDOI
Mean Field Games
TL;DR: In this paper, the authors present three examples of the mean-field approach to modelling in economics and finance (or other related subjects) and show that these nonlinear problems are essentially well-posed problems with unique solutions.
Journal ArticleDOI
An Iterative Regularization Method for Total Variation-Based Image Restoration
TL;DR: A new iterative regularization procedure for inverse problems based on the use of Bregman distances is introduced, with particular focus on problems arising in image processing.
Journal ArticleDOI
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
TL;DR: In this paper, the authors proposed simple and extremely efficient methods for solving the basis pursuit problem, which is used in compressed sensing, using Bregman iterative regularization, and they gave a very accurate solution after solving only a very small number of instances of the unconstrained problem.
Proceedings Article
A Kernel Method for the Two-Sample-Problem
TL;DR: This work proposes two statistical tests to determine if two samples are from different distributions, and applies this approach to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where the test performs strongly.
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