From Path Signatures to Sequential Modeling: Incremental Signature Contributions for Offline RL

Path signatures embed trajectories into tensor algebra and constitute a universal, non-parametric representation of paths; however, in the standard form, they collapse temporal structure into a single global object, which limits their suitability for decision-making problems that require step-wise reactivity. We propose the Incremental Signature Contribution (ISC) method, which decomposes truncated path signatures into a temporally ordered sequence of elements in the tensor-algebra space, corresponding to incremental contributions induced by last path increments. This reconstruction preserves the algebraic structure and expressivity of signatures, while making their internal temporal evolution explicit, enabling processing signature-based representations via sequential modeling approaches. In contrast to full signatures, ISC is inherently sensitive to instantaneous trajectory updates, which is critical for sensitive and stability-requiring control dynamics. Building on this representation, we introduce ISC-Transformer (ISCT), an offline reinforcement learning model that integrates ISC into a standard Transformer architecture without further architectural modification. We evaluate ISCT on HalfCheetah, Walker2d, Hopper, and Maze2d, including settings with delayed rewards and downgraded datasets. The results demonstrate that ISC method provides a theoretically grounded and practically effective alternative to path processing for temporally sensitive control tasks.

An Real-Sim-Real (RSR) Loop Framework for Generalizable Robotic Policy Transfer with Differentiable Simulation

The sim-to-real gap remains a critical challenge in robotics, hindering the deployment of algorithms trained in simulation to real-world systems. This paper introduces a novel Real-Sim-Real (RSR) loop framework leveraging differentiable simulation to address this gap by iteratively refining simulation parameters, aligning them with real-world conditions, and enabling robust and efficient policy transfer. A key contribution of our work is the design of an informative cost function that encourages the collection of diverse and representative real-world data, minimizing bias and maximizing the utility of each data point for simulation refinement. This cost function integrates seamlessly into existing reinforcement learning algorithms (e.g., PPO, SAC) and ensures a balanced exploration of critical regions in the real domain. Furthermore, our approach is implemented on the versatile Mujoco MJX platform, and our framework is compatible with a wide range of robotic systems. Experimental results on several robotic manipulation tasks demonstrate that our method significantly reduces the sim-to-real gap, achieving high task performance and generalizability across diverse scenarios of both explicit and implicit environmental uncertainties.