# Computing the Reachability Value of Posterior-Deterministic POMDPs

arXiv: https://arxiv.org/abs/2602.07473 · HTML: https://mlsanity.com/paper/2602.07473/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 36 references that are in the map.
- First posted on arXiv 7 Feb 2026.

## Builds on (most cited first, 6 of 6)

- [Partially Observable Markov Decision Processes in Robotics: A Survey](https://mlsanity.com/paper/2209.10342/) (2022)
- [What is Decidable about Partially Observable Markov Decision Processes with ω-Regular Objectives](https://mlsanity.com/paper/1309.2802/) (2013)
- [Multiple-Environment Markov Decision Processes](https://mlsanity.com/paper/1405.4733/) (2014)
- [The Value Problem for Multiple-Environment MDPs with Parity Objective](https://mlsanity.com/paper/2504.15960/) (2025)
- [Revelations: A Decidable Class of POMDPs with Omega-Regular Objectives](https://mlsanity.com/paper/2412.12063/) (2024)
- [Decisiveness for countable MDPs and insights for NPLCSs and POMDPs](https://mlsanity.com/paper/2008.10426/) (2020)

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

- [On the Complexity Gap Between POMDPs and Multi-Environment POMDPs](https://mlsanity.com/paper/2610.15010/) (2026)

## Abstract (arXiv)

Partially observable Markov decision processes (POMDPs) are a fundamental model for sequential decision-making under uncertainty. However, many verification and synthesis problems for POMDPs are undecidable or intractable. Most prominently, the seminal result of Madani et al. (2003) states that there is no algorithm that, given a POMDP and a set of target states, can compute the maximal probability of reaching the target states, or even approximate it up to a non-trivial constant. This is in stark contrast to fully observable Markov decision processes (MDPs), where the reachability value can be computed in polynomial time. In this work, we introduce posterior-deterministic POMDPs, a novel class of POMDPs. Our main technical contribution is to show that for posterior-deterministic POMDPs, the maximal probability of reaching a given set of states can be approximated up to arbitrary precision. A POMDP is posterior-deterministic if the next state can be uniquely determined by the current state, the action taken, and the observation received. While the actual state is generally uncertain in POMDPs, the posterior-deterministic property tells us that once the true state is known it remains known forever. This simple and natural definition includes all MDPs and captures classical non-trivial examples such as the Tiger POMDP (Kaelbling et al. 1998), making it one of the largest known classes of POMDPs for which the reachability value can be approximated.