# Anytime Probabilistically Constrained Provably Convergent Online Belief Space Planning

arXiv: https://arxiv.org/abs/2411.06711 · HTML: https://mlsanity.com/paper/2411.06711/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 11 Nov 2024.

## Builds on (most cited first, 11 of 11)

- [Online algorithms for POMDPs with continuous state, action, and observation spaces](https://mlsanity.com/paper/1709.06196/) (2017)
- [Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functions](https://mlsanity.com/paper/2010.16001/) (2020)
- [Optimality Guarantees for Particle Belief Approximation of POMDPs](https://mlsanity.com/paper/2210.05015/) (2022)
- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [ConstrainedZero: Chance-Constrained POMDP Planning using Learned Probabilistic Failure Surrogates and Adaptive Safety Constraints](https://mlsanity.com/paper/2405.00644/) (2024)
- [Online Planning for Constrained POMDPs with Continuous Spaces through Dual Ascent](https://mlsanity.com/paper/2212.12154/) (2022)
- [Shielding in Resource-Constrained Goal POMDPs](https://mlsanity.com/paper/2211.15349/) (2022)
- [Simplified Continuous High Dimensional Belief Space Planning with Adaptive Probabilistic Belief-dependent Constraints](https://mlsanity.com/paper/2302.06697/) (2023)
- [Risk Aware Adaptive Belief-dependent Probabilistically Constrained Continuous POMDP Planning](https://mlsanity.com/paper/2209.02679/) (2022)
- [Recursively-Constrained Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2310.09688/) (2023)
- [Constrained Hierarchical Monte Carlo Belief-State Planning](https://mlsanity.com/paper/2310.20054/) (2023)

## Abstract (arXiv)

Taking into account future risk is essential for an autonomously operating robot to find online not only the best but also a safe action to execute. In this paper, we build upon the recently introduced formulation of probabilistic belief-dependent constraints. We present an anytime approach employing the Monte Carlo Tree Search (MCTS) method in continuous domains. Unlike previous approaches, our method assures safety anytime with respect to the currently expanded search tree without relying on the convergence of the search. We prove convergence in probability with an exponential rate of a version of our algorithms and study proposed techniques via extensive simulations. Even with a tiny number of tree queries, the best action found by our approach is much safer than the baseline. Moreover, our approach constantly finds better than the baseline action in terms of objective. This is because we revise the values and statistics maintained in the search tree and remove from them the contribution of the pruned actions.