• Corpus ID: 252383586

Deep Generalized Schr\"odinger Bridge

  title={Deep Generalized Schr\"odinger Bridge},
  author={Guan-Horng Liu and Tian Qi Chen and Oswin So and Evangelos A. Theodorou},
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… 

Figures and Tables from this paper

Deep Multi-Marginal Momentum Schrödinger Bridge

This article extends SB into phase space and proposes Deep Momentum Multi-Marginal Schrödinger Bridge (DMSB), a novel computational framework that learns the smooth measure-valued spline for stochastic systems that satisfy position marginal constraints across time.

Alternating the population and control neural networks to solve high-dimensional stochastic mean-field games

APAC-Net is presented, an alternating population and agent control neural network for solving stochastic mean-field games (MFGs) that is geared toward high-dimensional instances of MFGs that are not approachable with existing solution methods.

Likelihood Training of Schrödinger Bridge using Forward-Backward SDEs Theory

A novel computational framework for likelihood training of SB models grounded on Forward-Backward Stochastic Differential Equations Theory - a mathematical methodology appeared in stochastic optimal control that transforms the optimality condition of SB into a set of SDEs that generalizes the ones for SGM as special cases.

A mean-field optimal control formulation of deep learning

This paper introduces the mathematical formulation of the population risk minimization problem in deep learning as a mean-field optimal control problem, and state and prove optimality conditions of both the Hamilton–Jacobi–Bellman type and the Pontryagin type.

A machine learning framework for solving high-dimensional mean field game and mean field control problems

This paper provides a flexible machine learning framework for the numerical solution of potential MFG and MFC models by combining Lagrangian and Eulerian viewpoints and leveraging recent advances from machine learning.

Deep Generative Learning via Schrödinger Bridge

The theoretical results guarantee that the distribution learned by the approach converges to the target distribution and indicate that the generative model via Schr\"{o}dinger Bridge is comparable with state-of-the-art GANs, suggesting a new formulation of generative learning.

A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth

A mean-field analysis of deep residual networks, based on a line of works that interpret the continuum limit of the deep residual network as an ordinary differential equation when the network capacity tends to infinity, and proposes a new continuum limit, which enjoys a good landscape in the sense that every local minimizer is global.

Recovering Stochastic Dynamics via Gaussian Schrödinger Bridges

We propose a new framework to reconstruct a stochastic process {Pt : t ∈ [0, T ]} using only samples from its marginal distributions, observed at start and end times 0 and T . This reconstruction is

Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling

Diffusion SB (DSB), an original approximation of the Iterative Proportional Fitting (IPF) procedure to solve the SB problem, is presented, and theoretical analysis along with generative modeling experiments are provided.

Mean field games

Abstract.We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field

Efficient computation of optimal actions

  • E. Todorov
  • Computer Science
    Proceedings of the National Academy of Sciences
  • 2009
This work proposes a more structured formulation that greatly simplifies the construction of optimal control laws in both discrete and continuous domains, and enables computations that were not possible before.