Generalized Schrödinger Bridge: From Generative Modeling to Mean-Field Games
The Schrödinger Bridge problem was originally introduced in the 1930s for quantum mechanics and later draws broader interests as an entropy-regularized optimal transport problem. In this seminar, I will talk about recent developments of SB as a new class of diffusion models and demonstrate their advantages in (i) generalizing standard score-based models to accepting nonlinear forward diffusions and (ii) solving distributionally constrained mean-field games with an order of magnitude higher dimension than prior methods. Central to our approach is the application of Forward-Backward SDEs theory (i.e., nonlinear Feynman Kac lemma), which provides a variational formulation of the optimality conditions and paves new connections to likelihood training and Temporal Difference learning. As such, it opens up new algorithmic opportunities in between diffusion models (as Neural SDEs), deep reinforcement learning, and regularized optimal transport.
Guan-Horng Liu is a PhD student in Machine Learning at the Georgia Tech supervised by Evangelos Theodorou. He was previously a Master’s student at the Robotics Institute of CMU. His research lies in scalable computational methods for Neural differential equations using stochastic optimal control, higher-order methods, and regularized optimal transport. His papers have been awarded with spotlight/oral presentations in ICLR'21, ICML'21, NeurIPS'21 '22. He is currently supported by the Graduate Fellowship from the Daniel Guggenheim School of Aerospace Engineering at Georgia Tech.
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