We study finite‑horizon partially observable Markov decision processes (POMDPs) with finite state, action, and observation spaces. In this setting both exact and approximate planning are known to be computationally hard, so prior work has sought natural assumptions that simplify planning. Recent work [Golowich et al., 2022] gave quasipolynomial‑time approximate planning algorithms for observable POMDPs, i.e., those whose observation channel satisfies an $\ell_1$‑observability condition, without imposing any restrictions on the transition dynamics. Following this line, for every fixed $\rho>0$ we present quasipolynomial‑time approximate planning algorithms for $\rho$‑decodable POMDPs. We show that decodability is implied by both $\ell_1$‑ and $\ell_2$‑observability and is strictly weaker than observability. Moreover, the optimal decodability constant can be computed in polynomial time, whereas computing the optimal $\ell_1$‑observability constant is NP‑hard in the worst case. We also demonstrate that the fast filter‑forgetting guarantee underlying the approach of [Golowich et al., 2022] does not extend directly from $\ell_1$‑observability to constant $\ell_2$‑observability. Thus, decodability is an easy‑to‑check, unifying assumption under which quasipolynomial‑time approximate planning for POMDPs becomes feasible.
Review: Decodability offers a milder condition than traditional observability while retaining tractability, providing a fresh theoretical tool for scaling planning algorithms to large‑scale POMDPs.