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Beyond Propagation of Chaos: A Stochastic Algorithm for Mean Field Optimization

Series: CSA Faculty Colloquium

Speaker: Prof. Anant Raj, Assistant Professor,Department of Computer Science and Automation, Indian Institute of Science (IISc)

Date/Time: Jun 06 16:00:00

Location: CSA Auditorium, (Room No. 104, Ground Floor)

Abstract:
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with n particles. Analyzing these algorithms requires showing (a) that the finite-particle system converges and/or (b) that the resultant empirical distribution of the particles closely approximates the optimal distribution (i.e., propagation of chaos). However, establishing efficient sufficient conditions can be challenging, as the finite particle system may produce heavily dependent random variables.

In this work, we study the virtual particle stochastic approximation, originally introduced for Stein Variational Gradient Descent. This method can be viewed as a form of stochastic gradient descent in the Wasserstein space and can be implemented efficiently. In popular settings, we demonstrate that our algorithms output converges to the optimal distribution under conditions similar to those for the infinite particle limit, and it produces i.i.d. samples without the need to explicitly establish propagation of chaos bounds.

Speaker Bio:
Anant Raj is an Assistant Professor in the Department of Computer Science and Automation at the Indian Institute of Science (IISc). Previously, he was a Marie Skłodowska-Curie Fellow jointly hosted by Prof. Francis Bach (Inria) and Prof. Maxim Raginsky (UIUC). He earned his Ph.D. in Machine Learning from the Max Planck Institute for Intelligent Systems under Prof. Bernhard Scholkopf, and holds a B.Tech - M.Tech dual degree in Electrical Engineering from IIT Kanpur. His research focuses on machine learning theory, with interests in optimization, sampling, kernel methods, and resource-efficient learning. He is a recipient of the IEEE CDC 2024 Roberto Tempo Best Paper Award and the Google India Research Award 2024.

Host Faculty: Prof. Sumit Kumar Mandal