Minimax-Optimal Predictive Flow Matching under Distribution Drift

Key points

• We study this predictive problem for a fixed, possibly nonconvex, neural class, with dynamic regret against the best represented field of each round.1
• We propose DyProd-FM, which refits flow matching on dyadic historical prefixes and selects among the fits with a sleeping Prod master.1
• Without knowing any drift budget, it attains regret $\widetilde{O}(\min\{Nω+1,1+\sqrt{TΩ}\})$ in the relative velocity risk variation $Ω$ and $\widetilde{O}(\min\{Nμ+1,1+T^{1/3}Vμ^{2/3}\})$ in the target-law variation $Vμ=\sumt W2(μ{t+1},μt)$, up to approximation and fitting costs.1
• Matching lower bounds for fixed classes show that both rates are optimal in $T$ and in the budgets up to logarithmic factors.1

Sources (1)

• [1]Minimax-Optimal Predictive Flow Matching under Distribution Drift
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 08:22 PM

  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.

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