Exponential Hardness of Off-Policy Evaluation under History-Dependent Logging
Can a logged dataset visit every hidden state frequently and still be exponentially uninformative about a target policy's value? We show that it can when the logger depends on history. For every horizon $H \ge 3$, we construct two POMDPs with at most two latent states per stage, three actions, and a common logger with three memory states. Action coverage, belief coverage, and two behavior-marginal outcome-revealing conditions all have constants independent of $H$. Nevertheless, evaluating a known deterministic target policy to accuracy $1/8$ requires $Θ((3/2)^H \log(1/δ))$ logged episodes at confidence $1-δ$, for $0 < δ\le 1/4$, even when both candidate models are known. The mechanism is ...
| Authors | Pranaya Jajoo |
|---|---|
| Primary category | cs.LG |
| Published | 16 September 2026 |
| Last updated at source | 16 September 2026 |
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