# Risk Aware Adaptive Belief-dependent Probabilistically Constrained Continuous POMDP Planning

arXiv: https://arxiv.org/abs/2209.02679 · HTML: https://mlsanity.com/paper/2209.02679/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 6 Sep 2022.

## Builds on (most cited first, 9 of 9)

- [Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age](https://mlsanity.com/paper/1606.05830/) (2016)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [DESPOT: Online POMDP Planning with Regularization](https://mlsanity.com/paper/1609.03250/) (2016)
- [Online algorithms for POMDPs with continuous state, action, and observation spaces](https://mlsanity.com/paper/1709.06196/) (2017)
- [Non-Gaussian Risk Bounded Trajectory Optimization for Stochastic Nonlinear Systems in Uncertain Environments](https://mlsanity.com/paper/2203.03038/) (2022)
- [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)
- [Collision Probabilities for Continuous-Time Systems Without Sampling [with Appendices]](https://mlsanity.com/paper/2006.01109/) (2020)
- [Enough is Enough: Towards Autonomous Uncertainty-driven Stopping Criteria](https://mlsanity.com/paper/2204.10631/) (2022)

## Built on by (most cited first, 3 of 3)

- [Simplified Continuous High Dimensional Belief Space Planning with Adaptive Probabilistic Belief-dependent Constraints](https://mlsanity.com/paper/2302.06697/) (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)

## Abstract (arXiv)

Although risk awareness is fundamental to an online operating agent, it has received less attention in the challenging continuous domain and under partial observability. This paper presents a novel formulation and solution for risk-averse belief-dependent probabilistically constrained continuous POMDP. We tackle a demanding setting of belief-dependent reward and constraint operators. The probabilistic confidence parameter makes our formulation genuinely risk-averse and much more flexible than the state-of-the-art chance constraint. Our rigorous analysis shows that in the stiffest probabilistic confidence case, our formulation is very close to chance constraint. However, our probabilistic formulation allows much faster and more accurate adaptive acceptance or pruning of actions fulfilling or violating the constraint. In addition, with an arbitrary confidence parameter, we did not find any analogs to our approach. We present algorithms for the solution of our formulation in continuous domains. We also uplift the chance-constrained approach to continuous environments using importance sampling. Moreover, all our presented algorithms can be used with parametric and nonparametric beliefs represented by particles. Last but not least, we contribute, rigorously analyze and simulate an approximation of chance-constrained continuous POMDP. The simulations demonstrate that our algorithms exhibit unprecedented celerity compared to the baseline, with the same performance in terms of collisions.