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arXiv · 2007.05065

Strategy Complexity of Parity Objectives in Countable MDPs

Stefan Kiefer·Richard Mayr·Mahsa Shirmohammadi·Patrick Totzke
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Abstract

We study countably infinite MDPs with parity objectives. Unlike in finite MDPs, optimal strategies need not exist, and may require infinite memory if they do. We provide a complete picture of the exact strategy complexity of $\varepsilon$-optimal strategies (and optimal strategies, where they exist) for all subclasses of parity objectives in the Mostowski hierarchy. Either MD-strategies, Markov strategies, or 1-bit Markov strategies are necessary and sufficient, depending on the number of colors, the branching degree of the MDP, and whether one considers $\varepsilon$-optimal or optimal strategies. In particular, 1-bit Markov strategies are necessary and sufficient for $\varepsilon$-optimal (resp. optimal) strategies for general parity objectives.

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Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, Patrick Totzke. 2020-07-07. Strategy Complexity of Parity Objectives in Countable MDPs. https://arxiv.org/abs/2007.05065

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