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Stochastic Optimization in Semi-Discrete Optimal Transport: Convergence Analysis and Minimax Rate

arXiv — stat.ML•Thursday, October 30, 2025 at 4:00:00 AM
NeutralArtificial Intelligence
Recent research delves into the semi-discrete Optimal Transport (OT) problem, focusing on how a continuous source measure can be effectively transported to a discrete target measure. This study highlights the promising performance of Stochastic Gradient Descent (SGD) solvers in machine learning, while also addressing the ongoing uncertainty regarding their theoretical ability to approximate the OT map. Understanding these dynamics is crucial as it could enhance the efficiency of various applications in machine learning and optimization.
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