Answer by zeb for Is Bayes optimal RL of a finite set of DFAs feasible?
Even determining whether there is a policy which always succeeds is NP-complete, by a reduction from constructing optimal decision trees (Hyafil and Rivest, Constructing Optimal Binary Decision Trees...
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Let $Q$ be a finite set of states, $\Sigma$ a finite alphabet, $q_0\in Q$ the start state and $F\subseteq Q$ the set of accepting sets. Let $\{\delta_k:Q\times\Sigma\rightarrow Q\}_{k=1}^n$ be a set of...
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