Deep Generalized Schrödinger Bridge

by   Guan-Horng Liu, et al.

Mean-Field Game (MFG) serves as a crucial mathematical framework in modeling the collective behavior of individual agents interacting stochastically with a large population. In this work, we aim at solving a challenging class of MFGs in which the differentiability of these interacting preferences may not be available to the solver, and the population is urged to converge exactly to some desired distribution. These setups are, despite being well-motivated for practical purposes, complicated enough to paralyze most (deep) numerical solvers. Nevertheless, we show that Schrödinger Bridge - as an entropy-regularized optimal transport model - can be generalized to accepting mean-field structures, hence solving these MFGs. This is achieved via the application of Forward-Backward Stochastic Differential Equations theory, which, intriguingly, leads to a computational framework with a similar structure to Temporal Difference learning. As such, it opens up novel algorithmic connections to Deep Reinforcement Learning that we leverage to facilitate practical training. We show that our proposed objective function provides necessary and sufficient conditions to the mean-field problem. Our method, named Deep Generalized Schrödinger Bridge (DeepGSB), not only outperforms prior methods in solving classical population navigation MFGs, but is also capable of solving 1000-dimensional opinion depolarization, setting a new state-of-the-art numerical solver for high-dimensional MFGs. Our code will be made available at


page 1

page 2

page 3

page 4


Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence

One of the core problems in mean-field control and mean-field games is t...

A synchronization-capturing multi-scale solver to the noisy integrate-and-fire neuron networks

The noisy leaky integrate-and-fire (NLIF) model describes the voltage co...

A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems

Mean field games (MFG) and mean field control (MFC) are critical classes...

Learning Deep Mean Field Games for Modeling Large Population Behavior

We consider the problem of representing collective behavior of large pop...

Deep Mean Field Games for Learning Optimal Behavior Policy of Large Populations

We consider the problem of representing a large population's behavior po...

Mean Field Games of Controls: Finite Difference Approximations

We consider a class of mean field games in which the agents interact thr...

Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularization

Mean-field games (MFGs) are a modeling framework for systems with a larg...

Please sign up or login with your details

Forgot password? Click here to reset