# Simplified decision making in the belief space using belief sparsification

arXiv: https://arxiv.org/abs/1909.00885 · HTML: https://mlsanity.com/paper/1909.00885/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2019.

## Built on by (most cited first, 10 of 10)

- [Simplified Belief-Dependent Reward MCTS Planning with Guaranteed Tree Consistency](https://mlsanity.com/paper/2105.14239/) (2021)
- [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)
- [Online POMDP Planning via Simplification](https://mlsanity.com/paper/2105.05296/) (2021)
- [Simplified Continuous High Dimensional Belief Space Planning with Adaptive Probabilistic Belief-dependent Constraints](https://mlsanity.com/paper/2302.06697/) (2023)
- [Probabilistic Loss and its Online Characterization for Simplified Decision Making Under Uncertainty](https://mlsanity.com/paper/2105.05789/) (2021)
- [Measurement Simplification in ρ-POMDP with Performance Guarantees](https://mlsanity.com/paper/2309.10701/) (2023)
- [No Compromise in Solution Quality: Speeding Up Belief-dependent Continuous POMDPs via Adaptive Multilevel Simplification](https://mlsanity.com/paper/2310.10274/) (2023)
- [Efficient Belief Space Planning in High-Dimensional State Spaces using PIVOT: Predictive Incremental Variable Ordering Tactic](https://mlsanity.com/paper/2112.14428/) (2021)
- [Towards Optimal Performance and Action Consistency Guarantees in Dec-POMDPs with Inconsistent Beliefs and Limited Communication](https://mlsanity.com/paper/2512.20778/) (2025)

## Abstract (arXiv)

In this work, we introduce a new and efficient solution approach for the problem of decision making under uncertainty, which can be formulated as decision making in a belief space, over a possibly high-dimensional state space. Typically, to solve a decision problem, one should identify the optimal action from a set of candidates, according to some objective. We claim that one can often generate and solve an analogous yet simplified decision problem, which can be solved more efficiently. A wise simplification method can lead to the same action selection, or one for which the maximal loss in optimality can be guaranteed. Furthermore, such simplification is separated from the state inference and does not compromise its accuracy, as the selected action would finally be applied on the original state. First, we present the concept for general decision problems and provide a theoretical framework for a coherent formulation of the approach. We then practically apply these ideas to decision problems in the belief space, which can be simplified by considering a sparse approximation of their initial belief. The scalable belief sparsification algorithm we provide is able to yield solutions which are guaranteed to be consistent with the original problem. We demonstrate the benefits of the approach in the solution of a realistic active-SLAM problem and manage to significantly reduce computation time, with no loss in the quality of solution. This work is both fundamental and practical, and holds numerous possible extensions.