Counterfactual equivalence for POMDPs, and underlying deterministic
  environments
  Partially Observable Markov Decision Processes (POMDPs) are rich environments
often used in machine learning. But the issue of information and causal
structures in POMDPs has been relatively little studied. This paper presents
the concepts of equivalent and counterfactually equivalent POMDPs, where agents
cannot distinguish which environment they are in though any observations and
actions. It shows that any POMDP is counterfactually equivalent, for any finite
number of turns, to a deterministic POMDP with all uncertainty concentrated
into the initial state. This allows a better understanding of POMDP
uncertainty, information, and learning.
