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

We study Learning to Defer for non-stationary time series with partial feedback and time-varying expert availability. At each time step, the router selects an available expert, observes the target, and sees only the queried expert's prediction. We model signed expert residuals using L2D-SLDS, a factorized switching linear-Gaussian state-space model with context-dependent regime transitions, a shared global factor enabling cross-expert information transfer, and per-expert idiosyncratic states. The model supports expert entry and pruning via a dynamic registry. Using one-step-ahead predictive beliefs, we propose an IDS-inspired routing rule that trades off predicted cost against information gained about the latent regime and shared factor. Experiments show improvements over contextual-bandit baselines and a no-shared-factor ablation.