# Simplified Continuous High Dimensional Belief Space Planning with Adaptive Probabilistic Belief-dependent Constraints

arXiv: https://arxiv.org/abs/2302.06697 · HTML: https://mlsanity.com/paper/2302.06697/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 51 references that are in the map.
- First posted on arXiv 13 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age](https://mlsanity.com/paper/1606.05830/) (2016)
- [Online algorithms for POMDPs with continuous state, action, and observation spaces](https://mlsanity.com/paper/1709.06196/) (2017)
- [A Survey on Active Simultaneous Localization and Mapping: State of the Art and New Frontiers](https://mlsanity.com/paper/2207.00254/) (2022)
- [Simplified decision making in the belief space using belief sparsification](https://mlsanity.com/paper/1909.00885/) (2019)
- [iX-BSP: Incremental Belief Space Planning](https://mlsanity.com/paper/2102.09539/) (2021)
- [Simplified Belief-Dependent Reward MCTS Planning with Guaranteed Tree Consistency](https://mlsanity.com/paper/2105.14239/) (2021)
- [Adaptive Information Belief Space Planning](https://mlsanity.com/paper/2201.05673/) (2022)
- [D2A-BSP: Distilled Data Association Belief Space Planning with Performance Guarantees Under Budget Constraints](https://mlsanity.com/paper/2202.04954/) (2022)
- [Nonmyopic Distilled Data Association Belief Space Planning Under Budget Constraints](https://mlsanity.com/paper/2207.08096/) (2022)
- [Topological Information-Theoretic Belief Space Planning with Optimality Guarantees](https://mlsanity.com/paper/1903.00927/) (2019)
- [Risk Aware Adaptive Belief-dependent Probabilistically Constrained Continuous POMDP Planning](https://mlsanity.com/paper/2209.02679/) (2022)
- [Enough is Enough: Towards Autonomous Uncertainty-driven Stopping Criteria](https://mlsanity.com/paper/2204.10631/) (2022)

## Built on by (most cited first, 4 of 4)

- [Data Association Aware POMDP Planning with Hypothesis Pruning Performance Guarantees](https://mlsanity.com/paper/2303.02139/) (2023)
- [No Compromise in Solution Quality: Speeding Up Belief-dependent Continuous POMDPs via Adaptive Multilevel Simplification](https://mlsanity.com/paper/2310.10274/) (2023)
- [Anytime Probabilistically Constrained Provably Convergent Online Belief Space Planning](https://mlsanity.com/paper/2411.06711/) (2024)
- [Scalable Rao-Blackwellized Online Planning for High-Dimensional POMDPs](https://mlsanity.com/paper/2609.01351/) (2026)

## Abstract (arXiv)

Online decision making under uncertainty in partially observable domains, also known as Belief Space Planning, is a fundamental problem in robotics and Artificial Intelligence. Due to an abundance of plausible future unravelings, calculating an optimal course of action inflicts an enormous computational burden on the agent. Moreover, in many scenarios, e.g., information gathering, it is required to introduce a belief-dependent constraint. Prompted by this demand, in this paper, we consider a recently introduced probabilistic belief-dependent constrained POMDP. We present a technique to adaptively accept or discard a candidate action sequence with respect to a probabilistic belief-dependent constraint, before expanding a complete set of future observations samples and without any loss in accuracy. Moreover, using our proposed framework, we contribute an adaptive method to find a maximal feasible return (e.g., information gain) in terms of Value at Risk for the candidate action sequence with substantial acceleration. On top of that, we introduce an adaptive simplification technique for a probabilistically constrained setting. Such an approach provably returns an identical-quality solution while dramatically accelerating online decision making. Our universal framework applies to any belief-dependent constrained continuous POMDP with parametric beliefs, as well as nonparametric beliefs represented by particles. In the context of an information-theoretic constraint, our presented framework stochastically quantifies if a cumulative information gain along the planning horizon is sufficiently significant (e.g. for, information gathering, active SLAM). We apply our method to active SLAM, a highly challenging problem of high dimensional Belief Space Planning. Extensive realistic simulations corroborate the superiority of our proposed ideas.