# Mixing Probabilistic and non-Probabilistic Objectives in Markov Decision Processes

arXiv: https://arxiv.org/abs/2004.13789 · HTML: https://mlsanity.com/paper/2004.13789/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2020.

## Built on by (most cited first, 1 of 1)

- [Rational Verification for Probabilistic Systems](https://mlsanity.com/paper/2107.09119/) (2021)

## Abstract (arXiv)

In this paper, we consider algorithms to decide the existence of strategies in MDPs for Boolean combinations of objectives. These objectives are omega-regular properties that need to be enforced either surely, almost surely, existentially, or with non-zero probability. In this setting, relevant strategies are randomized infinite memory strategies: both infinite memory and randomization may be needed to play optimally. We provide algorithms to solve the general case of Boolean combinations and we also investigate relevant subcases. We further report on complexity bounds for these problems.