From Path Signatures to Sequential Modeling: Incremental Signature Contributions for Offline RL
This work addresses the need for step-wise reactivity in control tasks for offline RL, offering an incremental improvement over existing path signature methods.
The paper tackled the problem of path signatures collapsing temporal structure in offline reinforcement learning by proposing the Incremental Signature Contribution (ISC) method to decompose them into a temporally ordered sequence, and introduced ISC-Transformer (ISCT) which demonstrated effectiveness on tasks like HalfCheetah and Maze2d with delayed rewards and downgraded datasets.
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.