Other types of corruption are more subtle. In CIRL, an irrational human may systematically take suboptimal actions in some situations [@Evans2016]. Depending on how we select stories in LVFS and make evaluations in SSRL, these may also be subject to systematic errors or biases.

The general impossibility result in \[th:impossibility\] can be adapted to CRMDPs with decoupled feedback. Without simplifying assumptions, the agent has no way of distinguishing between a situation where no state is corrupt and a situation where all states are corrupt in a consistent manner. The following simplifying assumption is an adaptation of \[as:lim-cor\] to the decoupled feedback case.

[\[as:lim-cor\]$\bf '$]{}\[Decoupled feedback with limited reward corruption\] \[as:lim-cor-df\] A class of CRMDPs with decoupled feedback has *reward corruption limited by $\Ssafe\subseteq\S$ and $q\in\SetN$* if for all $\mu\in\M$

$\orf_s(s')=\irf(s')$ or $\#$ for all $s'\in\S$ and $s\in\Ssafe$, i.e. all states in $\Ssafe$ are non-corrupt, and \[as:safe-state-df\]

$\orf_s(s')=\irf(s')$ or $\#$ for all $s'\in\S$ for at least $|\Srisky|-q$ of the non-safe states $\Srisky=\S\setminus\Ssafe$, i.e. at most $q$ states are corrupt. \[as:lim-del-df\]

This assumption is natural for reward corruption stemming from sensory corruption. Since sensory corruption only depends on the current state, not the state being observed, it is plausible that some states 