arXiv:2606.18778v2 Announce Type: replace-cross Abstract: Online learning in non-stationary streams is often formulated as tracking a point estimate, although many applications require predicting the full data-generating distribution. We study online distributional prediction under drift and bounded causal adversarial corruption. Candidate laws are represented by variable-size latent cluster configurations that induce predictive distributions. A Gibbs quasi-posterior over configurations yields an online predictor by posterior averaging and can be sampled using reversible-jump MCMC. The method uses no stream likelihood but specifies a kernel-mixture predictive family. We evaluate cumulative Wasserstein-1 regret against the time-varying true law and study periodic restart, sliding-window, and exponential-discounting memory against full history. The bounds separate PAC-Bayesian complexity, corruption-sensitive posterior perturbation, and drift through $A_T^{\mathrm{OT}}=\sum_{t=2}^T W_2^2(p_{t-1}^*,p_t^*)$. Under bounded support, latent quadratic growth, predictive-map regularity, and localized-comparator assumptions, restart has sublinear high-probability cumulative regret when $0\le a<1$, $q,\zeta,b<1$, $0\le\gamma<\beta<1$, and $0Source：https://arxiv.org/abs/2606.18778
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