[Submitted on 20 Oct 2026]
Abstract:Flow matching learns a generative velocity field by regression, but under distribution drift a field must be deployed before the current data arrive. We study this predictive problem for a fixed, possibly nonconvex, neural class, with dynamic regret against the best represented field of each round. We propose DyProd-FM, which refits flow matching on dyadic historical prefixes and selects among the fits with a sleeping Prod master. Without knowing any drift budget, it attains regret $widetilde{O}(min{N_omega+1,1+sqrt{TOmega}})$ in the relative velocity risk variation $Omega$ and $widetilde{O}(min{N_mu+1,1+T^{1/3}V_mu^{2/3}})$ in the target-law variation $V_mu=sum_t W_2(mu_{t+1},mu_t)$, up to approximation and fitting costs. Matching lower bounds for fixed classes show that both rates are optimal in $T$ and in the budgets up to logarithmic factors. Prior optimal dynamic-regret guarantees rely on a convex decision set with strongly convex or exp-concave losses, whereas our class may be nonconvex and no curvature in its parameters is assumed. The target-law rate rests on a second-order link between the two variations, which the base noise of flow matching provides.
Submission history
From: Aadithya Srikanth [view email]
[v1] Tue, 20 Oct 2026 20:22:37 UTC (72 KB)
