# Sparse tree search optimality guarantees in POMDPs with continuous observation spaces

arXiv: https://arxiv.org/abs/1910.04332 · HTML: https://mlsanity.com/paper/1910.04332/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2019.

## Built on by (most cited first, 7 of 7)

- [Optimality Guarantees for Particle Belief Approximation of POMDPs](https://mlsanity.com/paper/2210.05015/) (2022)
- [Compositional Learning-based Planning for Vision POMDPs](https://mlsanity.com/paper/2112.09456/) (2021)
- [Online POMDP Planning with Anytime Deterministic Optimality Guarantees](https://mlsanity.com/paper/2310.01791/) (2023)
- [Simplifying Complex Observation Models in Continuous POMDP Planning with Probabilistic Guarantees and Practice](https://mlsanity.com/paper/2311.07745/) (2023)
- [Online Robust Planning under Model Uncertainty: A Sample-Based Approach](https://mlsanity.com/paper/2509.10162/) (2025)
- [Factored Online Planning in Many-Agent POMDPs](https://mlsanity.com/paper/2312.11434/) (2023)
- [Anticipating Oblivious Opponents in Stochastic Games](https://mlsanity.com/paper/2409.11671/) (2024)

## Abstract (arXiv)

Partially observable Markov decision processes (POMDPs) with continuous state and observation spaces have powerful flexibility for representing real-world decision and control problems but are notoriously difficult to solve. Recent online sampling-based algorithms that use observation likelihood weighting have shown unprecedented effectiveness in domains with continuous observation spaces. However there has been no formal theoretical justification for this technique. This work offers such a justification, proving that a simplified algorithm, partially observable weighted sparse sampling (POWSS), will estimate Q-values accurately with high probability and can be made to perform arbitrarily near the optimal solution by increasing computational power.