# Zero-Shot Policy Transfer in Reinforcement Learning using Buckingham's Pi Theorem

arXiv: https://arxiv.org/abs/2510.08768 · HTML: https://mlsanity.com/paper/2510.08768/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 10 of 10)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Transfer Learning in Deep Reinforcement Learning: A Survey](https://mlsanity.com/paper/2009.07888/) (2020)
- [Controlling Overestimation Bias with Truncated Mixture of Continuous Distributional Quantile Critics](https://mlsanity.com/paper/2005.04269/) (2020)
- [CrossQ: Batch Normalization in Deep Reinforcement Learning for Greater Sample Efficiency and Simplicity](https://mlsanity.com/paper/1902.05605/) (2019)
- [Transfer Learning in Robotics: An Upcoming Breakthrough? A Review of Promises and Challenges](https://mlsanity.com/paper/2311.18044/) (2023)
- [Leveraging Symmetry to Accelerate Learning of Trajectory Tracking Controllers for Free-Flying Robotic Systems](https://mlsanity.com/paper/2409.11238/) (2024)
- [Improving Controller Generalization with Dimensionless Markov Decision Processes](https://mlsanity.com/paper/2504.10006/) (2025)
- [Dimensionless Policies based on the Buckingham π Theorem: Is This a Good Way to Generalize Numerical Results?](https://mlsanity.com/paper/2307.15852/) (2023)

## Built on by (most cited first, 1 of 1)

- [Direct transfer of optimized controllers to similar systems using dimensionless MPC](https://mlsanity.com/paper/2512.08667/) (2025)

## Abstract (arXiv)

Reinforcement learning (RL) policies often fail to generalize to new robots, tasks, or environments with different physical parameters, a challenge that limits their real-world applicability. This paper presents a simple, zero-shot transfer method based on Buckingham's Pi Theorem to address this limitation. The method adapts a pre-trained policy to new system contexts by scaling its inputs (observations) and outputs (actions) through a dimensionless space, requiring no retraining. The approach is evaluated against a naive transfer baseline across three environments of increasing complexity: a simulated pendulum, a physical pendulum for sim-to-real validation, and the high-dimensional HalfCheetah. Results demonstrate that the scaled transfer exhibits no loss of performance on dynamically similar contexts. Furthermore, on non-similar contexts, the scaled policy consistently outperforms the naive transfer, significantly expanding the volume of contexts where the original policy remains effective. These findings demonstrate that dimensional analysis provides a powerful and practical tool to enhance the robustness and generalization of RL policies.