Regime-Arrival Uncertainty in Generalization Bounds under Distribution Shift

Researchers have proposed new frameworks to improve understanding of how learning algorithms generalize under distribution shifts and regime changes.

Two separate research papers submitted to arXiv on June 1 and June 5, 2026, present novel approaches to addressing limitations in standard generalization bounds. The first paper^[1] focuses on regime composition mismatch in distribution shifts, proposing a framework that quantifies the extra risk due to differences in the ratio of calm versus crisis states between training and deployment distributions. This framework separates regime mismatch from regime sensitivity and extends the bound to beta-mixing data. The second paper^[2] introduces a stability-based framework that requires only a finite $L_p$ moment condition for understanding generalization of learning algorithms, moving beyond the classical assumptions of uniform boundedness or sub-Gaussian/sub-Weibull tails. The new framework applies to various learning paradigms, including empirical risk minimization, transductive regression, and meta-learning, and shows that $L_p$ stability suffices for robust generalization even when boundedness fails.