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

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.