A Game-Theoretic Framework for Generic Second-Order Traffic Flow Models Using Mean Field Games and Adversarial Inverse Reinforcement Learning

Zhaobin Mo (), Xu Chen (), Xuan Di (), Elisa Iacomini (), Chiara Segala (), Michael Herty () and Mathieu Lauriere ()
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Zhaobin Mo: Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027
Xu Chen: Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027
Xuan Di: Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027; Data Science Institute, Columbia University, New York, New York 10027
Elisa Iacomini: Mathematics and Computer Science Department, University of Ferrara, 44121 Ferrara, Italy
Chiara Segala: Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, 52062 Aachen, Germany
Michael Herty: Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, 52062 Aachen, Germany
Mathieu Lauriere: Institute of Mathematical Sciences, New York University, Shanghai 200122, China

Transportation Science, 2024, vol. 58, issue 6, 1403-1426

Abstract: A traffic system can be interpreted as a multiagent system, wherein vehicles choose the most efficient driving approaches guided by interconnected goals or strategies. This paper aims to develop a family of mean field games (MFG) for generic second-order traffic flow models (GSOM), in which cars control individual velocity to optimize their objective functions. GSOMs do not generally assume that cars optimize self-interested objectives, so such a game-theoretic reinterpretation offers insights into the agents’ underlying behaviors. In general, an MFG allows one to model individuals on a microscopic level as rational utility-optimizing agents while translating rich microscopic behaviors to macroscopic models. Building on the MFG framework, we devise a new class of second-order traffic flow MFGs (i.e., GSOM-MFG), which control cars’ acceleration to ensure smooth velocity change. A fixed-point algorithm with fictitious play technique is developed to solve GSOM-MFG numerically. In numerical examples, different traffic patterns are presented under different cost functions. For real-world validation, we further use an inverse reinforcement learning approach (IRL) to uncover the underlying cost function on the next-generation simulation (NGSIM) data set. We formulate the problem of inferring cost functions as a min-max game and use an apprenticeship learning algorithm to solve for cost function coefficients. The results show that our proposed GSOM-MFG is a generic framework that can accommodate various cost functions. The Aw Rascle and Zhang (ARZ) and Light-Whitham-Richards (LWR) fundamental diagrams in traffic flow models belong to our GSOM-MFG when costs are specified.

Keywords: mean field game (MFG); generic second order traffic flow model; adversarial inverse reinforcement learning (AIRL) (search for similar items in EconPapers)
Date: 2024
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