Continuous-time Online Learning via Mean-Field Neural Networks: Regret Analysis in Diffusion Environments
We study continuous-time online learning where data are generated by a diffusion process with unknown coefficients. The learner employs a two-layer neural network, continuously updating its parameters in a non-anticipative manner. The mean-field limit of the learning dynamics corresponds to a stochastic Wasserstein gradient flow adapted to the data filtration. We establish regret bounds for both the mean-field limit and finite-particle system. Our analysis leverages the logarithmic Sobolev inequality, Polyak-Lojasiewicz condition, Malliavin calculus, and uniform-in-time propagation of chaos. Under displacement convexity, we obtain a constant static regret bound. In the general non-convex ...
| Authors | Erhan Bayraktar, Bingyan Han, Ziqing Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 13 April 2026 |
| Last updated at source | 13 April 2026 |
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