# B"uchi Objectives in Countable MDPs

arXiv: https://arxiv.org/abs/1904.11573 · HTML: https://mlsanity.com/paper/1904.11573/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2019.

## Built on by (most cited first, 2 of 2)

- [Strategy Complexity of Point Payoff, Mean Payoff and Total Payoff Objectives in Countable MDPs](https://mlsanity.com/paper/2203.07079/) (2022)
- [Strategy Complexity of Mean Payoff, Total Payoff and Point Payoff Objectives in Countable MDPs](https://mlsanity.com/paper/2107.03287/) (2021)

## Abstract (arXiv)

We study countably infinite Markov decision processes with B"uchi objectives, which ask to visit a given subset of states infinitely often. A question left open by T.P. Hill in 1979 is whether there always exist varepsilon-optimal Markov strategies, i.e., strategies that base decisions only on the current state and the number of steps taken so far. We provide a negative answer to this question by constructing a non-trivial counterexample. On the other hand, we show that Markov strategies with only 1 bit of extra memory are sufficient.