Temporal Straightening for Latent Planning

Latent planning has emerged as a significant research direction in machine learning. By compressing high-dimensional observations into compact latent representations, latent planning improves efficiency and generalization. Early visual world models directly predicted in pixel spaces and used generated images for control. However, as research progressed, more methods began encoding high-dimensional sensory inputs into compact latent representations and planning in the resulting latent space. Existing methods typically add reconstruction-based objectives when training the encoder, but these objectives often overemphasize low-level visual details and may fail to capture task-relevant information. Recent approaches decouple perception from dynamics by leveraging strong pretrained visual encoders, yet these encoders are not optimized for planning and may lead to challenging planning objectives.

Optimizing the learned latent space remains challenging in latent planning. The induced planning objective is typically highly non-convex, potentially causing gradient-based optimizers to struggle. Moreover, commonly used goal cost metrics based on Euclidean distance can be misleading if the embedding space is not properly regularized. In particular, when latent trajectories are highly curved, straight-line distances in embedding space misrepresent the geodesic distance along feasible transitions. These challenges call for better representations tailored for latent planning.

The paper introduces a novel representation learning method called Temporal Straightening, which optimizes the linearity of latent trajectories through curvature regularization. This method jointly trains an encoder and a predictor, making the Euclidean distance in latent space a better proxy for geodesic distance, thereby improving the conditioning of the planning objective. Specifically, curvature regularization is used to encourage locally straightened latent trajectories, enhancing the stability of gradient-based planning.

• �� Temporal Straightening optimizes the linearity of latent trajectories through curvature regularization.
• �� Jointly trains an encoder and a predictor, making the Euclidean distance in latent space a better proxy for geodesic distance.
• �� Uses curvature regularization to encourage locally straightened latent trajectories, enhancing the stability of gradient-based planning.
• �� Significantly improves success rates across a suite of goal-reaching tasks.

The experimental design includes evaluating planning performance across four environments: Wall, PointMaze UMaze, a medium-sized maze, and PushT. The experiments use frozen DINOv2 spatial features or CLS tokens. Following DINO-WM's setup, all environments use a frameskip of 5. Details on the environments and experiments are provided in the appendix of the paper. The results demonstrate the method's effectiveness across different tasks, especially in high-dimensional observation environments.

Experimental results show that open-loop planning success improves by 20-60%, and MPC by 20-30%. These results demonstrate the method's effectiveness across different tasks, especially in high-dimensional observation environments. Comparisons of different encoder and predictor architectures reveal that models trained from scratch with ResNet exhibit superior curvature reduction, further validating the effectiveness of the Temporal Straightening method.

Temporal Straightening is significant in the field of latent planning as it not only enhances planning stability and success rates but also offers a new perspective on representation learning. By reducing the curvature of latent trajectories, the method makes Euclidean distance a better proxy for geodesic distance, thereby improving the conditioning of planning objectives. This approach provides new insights for developing latent world models, particularly in high-dimensional observation environments, effectively reducing computational burdens and latency.

Despite its superior performance in multiple tasks, Temporal Straightening faces challenges in long-horizon planning tasks where prediction errors may accumulate, leading to trajectory drift. Additionally, in complex dynamic environments, the method may require higher computational resources to achieve real-time planning. Future research directions include verifying the effectiveness of Temporal Straightening in more complex 3D environments and exploring its applications in robotic planning.