Exposure Bias as Epistemic Underidentification in Recursive Forecasting
For researchers in time series forecasting and sequential decision-making, the paper reframes a known problem (exposure bias) in a new theoretical light, but the empirical gains are conditional and not uniform, making it an incremental theoretical contribution.
The paper proves that exposure bias in recursive forecasting is not just distribution shift but an epistemic underidentification problem under partial observability. It introduces provenance variables to decompose induced-state error and shows that provenance-aware correction can improve performance, though gains are conditional.
Recursive multi-step forecasting is usually framed as distribution shift: models are trained on observed histories but deployed on their own predictions. We show this framing is incomplete by proving that, under partial observability or state truncation, recursive rollout is also an epistemic underidentification problem. Even with deterministic latent dynamics, one-step Bayes supervision identifies behavior only on observed contexts and need not identify the deployed recursive predictor once rollout queries self-generated induced states whose correct local targets are not determined by numeric state alone. We formalize this with induced states $Z$ and provenance variables $P$, and derive a decomposition of induced-state error into teacher-forcing/rollout mismatch, representation--class approximation, and provenance information gaps. Empirically, we show that rollout enters a distinct induced-state regime, that fixed induced states define a distinct local corrective task, and that closed-loop gains arise not only from local adaptation but also from changing the induced states visited during rollout. Using a simple binary provenance encoding, provenance-aware correction can further improve performance, though gains are conditional rather than uniform. These results recast exposure bias as reasoning under self-induced epistemic uncertainty.