Polynomial sample complexity for learning γ-observable POMDPs without privileged information

Determine whether a learning algorithm for γ-observable POMDPs in the standard reinforcement learning access model (without access to latent state information) can achieve polynomial, rather than quasi-polynomial, sample complexity, matching the improvement obtainable when latent state information is available.

Background

The paper reviews results showing that γ-observable POMDPs admit learning algorithms with quasi-polynomial complexity (Golowich et al., 2022).

Cai et al. (2024) showed that when privileged latent state information is available at training time, the sample complexity can be improved from quasi-polynomial to polynomial.

The authors explicitly note that whether such a polynomial sample complexity is attainable without latent state information remains an open question, highlighting a key theoretical gap between learning with and without privileged information.