Learning to Defer in Non-Stationary Time Series via Switching State-Space Models

Learning-to-defer (L2D) routes each decision to a system's own predictor or to an external expert. Streaming time-series settings break the offline-L2D assumptions: the data are non-stationary, expert availability shifts over time, and the internal predictor is trained online. We propose L2D-SLDS, a one-stage online L2D framework based on a factorized switching linear-Gaussian state-space model over all potential residuals: a discrete regime, a shared global factor, and per-expert idiosyncratic states. The always-observed internal residual continuously updates beliefs about every unqueried expert through the shared factor, and a learner-aware query score balances immediate cost against latent-state information gain and one-step learner improvement. We prove an oracle inequality against a time-varying learn-and-defer comparator, decomposing regret into a query-bonus budget, an SLDS predictive-cost-error term~$\mathcal{E}_{\mathrm{SLDS}}$, and the internal learner's interval dynamic regret. On synthetic, Melbourne, Jena, and 24-expert Delhi benchmarks, L2D-SLDS is competitive with or improves on contextual- and non-stationary-bandit baselines while deferring on ${<}2\%$ of real-data rounds.