# Sound Heuristic Search Value Iteration for Undiscounted POMDPs with Reachability Objectives

arXiv: https://arxiv.org/abs/2406.02871 · HTML: https://mlsanity.com/paper/2406.02871/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Builds on (most cited first, 10 of 10)

- [Partially Observable Markov Decision Processes in Robotics: A Survey](https://mlsanity.com/paper/2209.10342/) (2022)
- [Bandit Algorithms for Tree Search](https://mlsanity.com/paper/1408.2028/) (2014)
- [Inductive Synthesis of Finite-State Controllers for POMDPs](https://mlsanity.com/paper/2203.10803/) (2022)
- [Optimistic Value Iteration](https://mlsanity.com/paper/1910.01100/) (2019)
- [Point-Based Methods for Model Checking in Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2001.03809/) (2020)
- [Verification of indefinite-horizon POMDPs](https://mlsanity.com/paper/2007.00102/) (2020)
- [Under-Approximating Expected Total Rewards in POMDPs](https://mlsanity.com/paper/2201.08772/) (2022)
- [Optimal Control of Partially Observable Markov Decision Processes with Finite Linear Temporal Logic Constraints](https://mlsanity.com/paper/2203.09038/) (2022)
- [Search and Explore: Symbiotic Policy Synthesis in POMDPs](https://mlsanity.com/paper/2305.14149/) (2023)
- [Trust-Aware Motion Planning for Human-Robot Collaboration under Distribution Temporal Logic Specifications](https://mlsanity.com/paper/2310.01163/) (2023)

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

- [Constrained and Robust Policy Synthesis with Satisfiability-Modulo-Probabilistic-Model-Checking](https://mlsanity.com/paper/2511.08078/) (2025)
- [Finite-State Controllers for (Hidden-Model) POMDPs using Deep Reinforcement Learning](https://mlsanity.com/paper/2602.08734/) (2026)

## Abstract (arXiv)

Partially Observable Markov Decision Processes (POMDPs) are powerful models for sequential decision making under transition and observation uncertainties. This paper studies the challenging yet important problem in POMDPs known as the (indefinite-horizon) Maximal Reachability Probability Problem (MRPP), where the goal is to maximize the probability of reaching some target states. This is also a core problem in model checking with logical specifications and is naturally undiscounted (discount factor is one). Inspired by the success of point-based methods developed for discounted problems, we study their extensions to MRPP. Specifically, we focus on trial-based heuristic search value iteration techniques and present a novel algorithm that leverages the strengths of these techniques for efficient exploration of the belief space (informed search via value bounds) while addressing their drawbacks in handling loops for indefinite-horizon problems. The algorithm produces policies with two-sided bounds on optimal reachability probabilities. We prove convergence to an optimal policy from below under certain conditions. Experimental evaluations on a suite of benchmarks show that our algorithm outperforms existing methods in almost all cases in both probability guarantees and computation time.