Title: Uncertainty Regarding Regime Arrival in Generalization Bounds Amidst Distribution Shift

Abstract: Conventional generalization bounds typically rely on the assumption that training and deployment distributions are identical or static, thereby overlooking environments characterized by regime switching where the proportion of calm versus crisis states fluctuates. To address this, we introduce a framework that extends regime-aware models by measuring the additional risk arising from mismatches in regime composition, specifically within Markov-switching distribution shifts. Our approach yields a precise decomposition that isolates regime mismatch from regime sensitivity. Furthermore, we adapt the bound to accommodate beta-mixing data by incorporating an effective sample size adjusted for the spectral gap. We validate these findings through minimax lower bounds derived from synthetic data and a 25-year dataset of global equity indices. Notably, the proposed penalty corresponds to the ex post realized generalization gap, a metric that contrasts with training-only estimators, which exhibit no significant correlation. While the feature geometry associated with crises can be identified, the temporal arrival of such events cannot. Consequently, this framework functions not as a forecasting tool. Predicting the composition of future regimes during rare regime changes remains an unresolved challenge.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC