Wavelet Policy: Lifting Scheme for Policy Learning in Long-Horizon Tasks

Policy learning focuses on devising strategies for agents in embodied artificial intelligence systems to perform optimal actions based on their perceived states. One of the key challenges in policy learning involves handling complex, longhorizon tasks that require managing extensive sequences of actions and observations with multiple modes. Wavelet analysis offers significant advantages in signal processing, notably in decomposing signals at multiple scales to capture both global trends and fine-grained details. In this work, we introduce a novel wavelet policy learning framework that utilizes wavelet transformations to enhance policy learning. Our approach leverages learnable multi-scale wavelet decomposition to facilitate detailed observation analysis and robust action planning over extended sequences. We detail the design and implementation of our wavelet policy, which incorporates lifting schemes for effective multiresolution analysis and action generation. This framework is evaluated across multiple complex scenarios, including robotic manipulation, self-driving, and multi-robot collaboration, demonstrating the effectiveness of our method in improving the precision and reliability of the learned policy. Our project is available at https://hhuang- code.github.io/wavelet_policy/.