Continuous-time Online Learning via Mean-Field Neural Networks: Regret Analysis in Diffusion Environments

ArXi:2604.10958v1 Announce Type: cross 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.