# Path Signatures for Diversity in Probabilistic Trajectory Optimisation

arXiv: https://arxiv.org/abs/2308.04071 · HTML: https://mlsanity.com/paper/2308.04071/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 62 references that are in the map.
- First posted on arXiv 8 Aug 2023.

## Builds on (most cited first, 22 of 22)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [The Signature Kernel is the solution of a Goursat PDE](https://mlsanity.com/paper/2006.14794/) (2020)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [Message Passing Stein Variational Gradient Descent](https://mlsanity.com/paper/1711.04425/) (2017)
- [Object Rearrangement Using Learned Implicit Collision Functions](https://mlsanity.com/paper/2011.10726/) (2020)
- [Stein Variational Model Predictive Control](https://mlsanity.com/paper/2011.07641/) (2020)
- [Embedding and learning with signatures](https://mlsanity.com/paper/1911.13211/) (2019)
- [Developing the Path Signature Methodology and its Application to Landmark-based Human Action Recognition](https://mlsanity.com/paper/1707.03993/) (2017)
- [MotionBenchMaker: A Tool to Generate and Benchmark Motion Planning Datasets](https://mlsanity.com/paper/2112.06402/) (2021)
- [PPO-CMA: Proximal Policy Optimization with Covariance Matrix Adaptation](https://mlsanity.com/paper/1810.02541/) (2018)
- [Dual Online Stein Variational Inference for Control and Dynamics](https://mlsanity.com/paper/2103.12890/) (2021)
- [DISCO: Double Likelihood-free Inference Stochastic Control](https://mlsanity.com/paper/2002.07379/) (2020)
- [Functional Gradient Motion Planning in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/1601.03648/) (2016)
- [A Gaussian variational inference approach to motion planning](https://mlsanity.com/paper/2209.05655/) (2022)
- [Entropy Regularized Motion Planning via Stein Variational Inference](https://mlsanity.com/paper/2107.05146/) (2021)

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

- [Learning Multiple Initial Solutions to Optimization Problems](https://mlsanity.com/paper/2411.02158/) (2024)
- [Stein Variational Evolution Strategies](https://mlsanity.com/paper/2410.10390/) (2024)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)

## Abstract (arXiv)

Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem is usually difficult to solve and prone to local minima. However, recent advancements in computing hardware allow for parallel trajectory optimisation where multiple solutions are obtained simultaneously, each initialised from a different starting point. Unfortunately, without a strategy preventing two solutions to collapse on each other, naive parallel optimisation can suffer from mode collapse diminishing the efficiency of the approach and the likelihood of finding a global solution. In this paper we leverage on recent advances in the theory of rough paths to devise an algorithm for parallel trajectory optimisation that promotes diversity over the range of solutions, therefore avoiding mode collapses and achieving better global properties. Our approach builds on path signatures and Hilbert space representations of trajectories, and connects parallel variational inference for trajectory estimation with diversity promoting kernels. We empirically demonstrate that this strategy achieves lower average costs than competing alternatives on a range of problems, from 2D navigation to robotic manipulators operating in cluttered environments.