Minimal Markovization via Stable Quotients in Holonomy-Cover Decision Processes
An agent acting under partial observability must retain a recursively updateable statistic of history that restores the Markov property, but the smallest such statistic is generally unknown. We characterize this minimal Markov sufficient statistic for holonomy-cover decision processes, a structured POMDP class in which the visible dynamics are Markov and every realized visible transition applies a fixed permutation to a hidden mode. In particular, we construct the stable quotient, the coarsest observation-wise abstraction preserving one-step rewards and quotient successors, and prove that the pair of the current observation and stable class forms an exact finite Markov state. When the cur...
| Authors | Zuyuan Zhang, Yongshan Chen, Mahdi Imani et al. |
|---|---|
| Primary category | cs.LG |
| Published | 29 July 2026 |
| Last updated at source | 29 July 2026 |
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