# Bingham Policy Parameterization for 3D Rotations in Reinforcement Learning

arXiv: https://arxiv.org/abs/2202.03957 · HTML: https://mlsanity.com/paper/2202.03957/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 38 references that are in the map.
- First posted on arXiv 8 Feb 2022.

## Builds on (most cited first, 21 of 21)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [RLBench: The Robot Learning Benchmark & Learning Environment](https://mlsanity.com/paper/1909.12271/) (2019)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [DenseFusion: 6D Object Pose Estimation by Iterative Dense Fusion](https://mlsanity.com/paper/1901.04780/) (2019)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [CosyPose: Consistent multi-view multi-object 6D pose estimation](https://mlsanity.com/paper/2008.08465/) (2020)
- [Sim-to-Real Reinforcement Learning for Deformable Object Manipulation](https://mlsanity.com/paper/1806.07851/) (2018)
- [Coarse-to-Fine Q-attention: Efficient Learning for Visual Robotic Manipulation via Discretisation](https://mlsanity.com/paper/2106.12534/) (2021)
- [Q-attention: Enabling Efficient Learning for Vision-based Robotic Manipulation](https://mlsanity.com/paper/2105.14829/) (2021)
- [MoreFusion: Multi-object Reasoning for 6D Pose Estimation from Volumetric Fusion](https://mlsanity.com/paper/2004.04336/) (2020)
- [Is Bang-Bang Control All You Need? Solving Continuous Control with Bernoulli Policies](https://mlsanity.com/paper/2111.02552/) (2021)
- [A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty](https://mlsanity.com/paper/2006.01031/) (2020)
- [Growing Action Spaces](https://mlsanity.com/paper/1906.12266/) (2019)
- [Cat-like Jumping and Landing of Legged Robots in Low-gravity Using Deep Reinforcement Learning](https://mlsanity.com/paper/2106.09357/) (2021)
- [Unscented Orientation Estimation Based on the Bingham Distribution](https://mlsanity.com/paper/1311.5796/) (2013)

## Built on by (most cited first, 8 of 8)

- [Coarse-to-Fine Q-attention with Learned Path Ranking](https://mlsanity.com/paper/2204.01571/) (2022)
- [Coarse-to-fine Q-attention with Tree Expansion](https://mlsanity.com/paper/2204.12471/) (2022)
- [Redundancy-aware Action Spaces for Robot Learning](https://mlsanity.com/paper/2406.04144/) (2024)
- [Kuramoto Oscillators and Swarms on Manifolds for Geometry Informed Machine Learning](https://mlsanity.com/paper/2405.09453/) (2024)
- [Non-parametric regression for robot learning on manifolds](https://mlsanity.com/paper/2310.19561/) (2023)
- [Reinforcement Learning in Hyperbolic Spaces: Models and Experiments](https://mlsanity.com/paper/2410.09466/) (2024)
- [L2Calib: SE(3)-Manifold Reinforcement Learning for Robust Extrinsic Calibration with Degenerate Motion Resilience](https://mlsanity.com/paper/2508.06330/) (2025)
- [Information-Geometric Optimization on Spheres](https://mlsanity.com/paper/2606.07588/) (2026)

## Abstract (arXiv)

We propose a new policy parameterization for representing 3D rotations during reinforcement learning. Today in the continuous control reinforcement learning literature, many stochastic policy parameterizations are Gaussian. We argue that universally applying a Gaussian policy parameterization is not always desirable for all environments. One such case in particular where this is true are tasks that involve predicting a 3D rotation output, either in isolation, or coupled with translation as part of a full 6D pose output. Our proposed Bingham Policy Parameterization (BPP) models the Bingham distribution and allows for better rotation (quaternion) prediction over a Gaussian policy parameterization in a range of reinforcement learning tasks. We evaluate BPP on the rotation Wahba problem task, as well as a set of vision-based next-best pose robot manipulation tasks from RLBench. We hope that this paper encourages more research into developing other policy parameterization that are more suited for particular environments, rather than always assuming Gaussian.