Paper Detail
Pranaya Jajoo
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 simple: a reset erases the unknown transition that determines the target value. We characterize the resulting statistical experiment exactly and obtain a matching optimal estimator. A directed two-lane gridworld realizes the construction, and trajectory simulations agree with its finite-sample prediction. The result establishes intractability for the history-dependent-logging, model-based case posed by Zhang and Jiang (2025, arXiv:2503.01134), under their behavior-marginal definition of revealing.
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@article{jajoo2026exponential,
title = {Exponential Hardness of Off-Policy Evaluation under History-Dependent Logging},
author = {Pranaya Jajoo},
year = {2026},
abstract = {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 \textbackslash{}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 know},
url = {https://arxiv.org/abs/2609.19135},
keywords = {cs.LG},
eprint = {2609.19135},
archiveprefix = {arXiv},
}
{}