For finite discounted MDPs, optimal actions under all state-action rewards identify transitions only up to an n(n-1)-dimensional matrix orbit, while transition-dependent rewards identify almost every strictly positive kernel exactly.
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From Optimal Actions to World Models: Identifiability of Transition Kernels in Discounted MDPs
For finite discounted MDPs, optimal actions under all state-action rewards identify transitions only up to an n(n-1)-dimensional matrix orbit, while transition-dependent rewards identify almost every strictly positive kernel exactly.