arXiv Machine Learning By Aadithya Srikanth, Vaneet Aggarwal

Minimax-Optimal Predictive Flow Matching under Distribution Drift

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The paper introduces DyProd-FM, a method for predictive flow matching that refits flow matching models on dyadic historical prefixes and selects among them using a sleeping Prod master. It achieves dynamic regret bounds of “~O(min{N_ω+1,1+√{TΩ}}) and ~O(min{N_μ+1,1+T^{1/3}V_μ^{2/3}}) in relative velocity risk variation Ω and target‑law variation V_μ, respectively, without requiring a drift budget. These bounds are shown to be optimal up to logarithmic factors for fixed, possibly nonconvex, neural classes.

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