23 research outputs found
Solving N-player dynamic routing games with congestion: a mean field approach
The recent emergence of navigational tools has changed traffic patterns and has now enabled new types of congestion-aware routing control like dynamic road pricing. Using the fundamental diagram of traffic flows - applied in macroscopic and mesoscopic traffic modeling - the article introduces a new N-player dynamic routing game with explicit congestion dynamics. The model is well-posed and can reproduce heterogeneous departure times and congestion spill back phenomena. However, as Nash equilibrium computations are PPAD-complete, solving the game becomes intractable for large but realistic numbers of vehicles N. Therefore, the corresponding mean field game is also introduced. Experiments were performed on several classical benchmark networks of the traffic community: the Pigou, Braess, and Sioux Falls networks with heterogeneous origin, destination and departure time tuples. The Pigou and the Braess examples reveal that the mean field approximation is generally very accurate and computationally efficient as soon as the number of vehicles exceeds a few dozen. On the Sioux Falls network (76 links, 100 time steps), this approach enables learning traffic dynamics with more than 14,000 vehicles
Solving N-player dynamic routing games with congestion: a mean field approach
The recent emergence of navigational tools has changed traffic patterns and has now enabled new types of congestion-aware routing control like dynamic road pricing. Using the fundamental diagram of traffic flows - applied in macroscopic and mesoscopic traffic modeling - the article introduces a new N-player dynamic routing game with explicit congestion dynamics. The model is well-posed and can reproduce heterogeneous departure times and congestion spill back phenomena. However, as Nash equilibrium computations are PPAD-complete, solving the game becomes intractable for large but realistic numbers of vehicles N. Therefore, the corresponding mean field game is also introduced. Experiments were performed on several classical benchmark networks of the traffic community: the Pigou, Braess, and Sioux Falls networks with heterogeneous origin, destination and departure time tuples. The Pigou and the Braess examples reveal that the mean field approximation is generally very accurate and computationally efficient as soon as the number of vehicles exceeds a few dozen. On the Sioux Falls network (76 links, 100 time steps), this approach enables learning traffic dynamics with more than 14,000 vehicles
Solving N-player dynamic routing games with congestion: a mean field approach
The recent emergence of navigational tools has changed traffic patterns and has now enabled new types of congestion-aware routing control like dynamic road pricing. Using the fundamental diagram of traffic flows - applied in macroscopic and mesoscopic traffic modeling - the article introduces a new N-player dynamic routing game with explicit congestion dynamics. The model is well-posed and can reproduce heterogeneous departure times and congestion spill back phenomena. However, as Nash equilibrium computations are PPAD-complete, solving the game becomes intractable for large but realistic numbers of vehicles N. Therefore, the corresponding mean field game is also introduced. Experiments were performed on several classical benchmark networks of the traffic community: the Pigou, Braess, and Sioux Falls networks with heterogeneous origin, destination and departure time tuples. The Pigou and the Braess examples reveal that the mean field approximation is generally very accurate and computationally efficient as soon as the number of vehicles exceeds a few dozen. On the Sioux Falls network (76 links, 100 time steps), this approach enables learning traffic dynamics with more than 14,000 vehicles
Scalable Deep Reinforcement Learning Algorithms for Mean Field Games
Mean Field Games (MFGs) have been introduced to efficiently approximate games
with very large populations of strategic agents. Recently, the question of
learning equilibria in MFGs has gained momentum, particularly using model-free
reinforcement learning (RL) methods. One limiting factor to further scale up
using RL is that existing algorithms to solve MFGs require the mixing of
approximated quantities such as strategies or -values. This is far from
being trivial in the case of non-linear function approximation that enjoy good
generalization properties, e.g. neural networks. We propose two methods to
address this shortcoming. The first one learns a mixed strategy from
distillation of historical data into a neural network and is applied to the
Fictitious Play algorithm. The second one is an online mixing method based on
regularization that does not require memorizing historical data or previous
estimates. It is used to extend Online Mirror Descent. We demonstrate
numerically that these methods efficiently enable the use of Deep RL algorithms
to solve various MFGs. In addition, we show that these methods outperform SotA
baselines from the literature
Systematic ultrasound examinations in neonates admitted to NICU: evolution of portal vein thrombosis
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