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No good Markov strategies for Büchi objectives in countable MDPs
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Abstract
We study countably infinite Markov decision processes with Büchi objectives, which ask to visit a given subset of states infinitely often. A question left open by T.P. Hill (1979) is whether there always exist
$$\varepsilon $$
ε
-optimal Markov strategies, i.e., strategies that base decisions only on the current state and on the clock (the number of steps taken so far). We provide a negative answer to this question by constructing a non-trivial counterexample.
Springer Science and Business Media LLC
Title: No good Markov strategies for Büchi objectives in countable MDPs
Description:
Abstract
We study countably infinite Markov decision processes with Büchi objectives, which ask to visit a given subset of states infinitely often.
A question left open by T.
P.
Hill (1979) is whether there always exist
$$\varepsilon $$
ε
-optimal Markov strategies, i.
e.
, strategies that base decisions only on the current state and on the clock (the number of steps taken so far).
We provide a negative answer to this question by constructing a non-trivial counterexample.
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