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Explore the optimization of Schrödinger Bridge (SB) in this 28-minute conference talk delivered at the Workshop on "One World Optimization Seminar in Vienna" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into a novel geometric framework for SB optimization, introducing a continuous-time adaptation of the Sinkhorn algorithm. Discover how this innovation leads to new Sinkhorn variants with variable step sizes, ensuring convergence even in noisy and biased environments. Examine the unique Riemannian geometric structure developed for probability measures, extending the classical Fisher-Rao metric to conditional variants. Learn how this methodology, leveraging its connection to mirror descent theory, results in an accelerated version of Sinkhorn dynamics. Gain insights into the significance of SB in AI frameworks like diffusion models and understand the challenges in developing efficient algorithmic solutions for this important optimization problem.
